Mathematics and Statistics

The theory of dynamic systems is addressed in this book in accordance with the “modern” approach, heir to algebraic analysis, which has been implemented since the last decade of the 20th century. After a reminder of the evolution of the representati... (Read more)

This book is devoted to the construction and study of approximate methods for solving mathematical physics problems in canonical domains. It focuses on obtaining weighted a priori estimates of the accuracy of these methods while also considering the influe... (Read more)

Many physical, chemical, biological and even economic phenomena can be modeled by differential or partial differential equations, and the framework of distribution theory is the most efficient way to study these equations. A solid familiarity with the lang... (Read more)

This book illustrates a number of asymptotic and analytic approaches applied for the study of random evolutionary systems, and considers typical problems for specific examples. In this case, constructive mathematical models of natural processes are used, w... (Read more)

From Pythagoreans to Hegel, and beyond, this book gives a brief overview of the history of the notion of graphs and introduces the main concepts of graph theory in order to apply them to philosophy. In addition, this book presents how philosophers can use ... (Read more)

Matrix-analytic methods (MAM) were introduced by Professor Marcel Neuts and have been applied to a variety of stochastic models since. In order to provide a clear and deep understanding of MAM while showing their power, this book presents MAM concepts a... (Read more)

Matrix-analytic methods (MAM) were introduced by Professor Marcel Neuts and have been applied to a variety of stochastic models since. In order to provide a clear and deep understanding of MAM while showing their power, this book presents MAM concepts a... (Read more)

This book presents a simple and original theory of distributions, both real and vector, adapted to the study of partial differential equations. It deals with value distributions in a Neumann space, that is, in which any Cauchy suite converges, which encomp... (Read more)

This book is devoted to the study of stochastic measures (SMs). An SM is a sigma-additive in probability random function, defined on a sigma-algebra of sets. SMs can be generated by the increments of random processes from many important classes such as squ... (Read more)

This book illustrates the powerful interplay between topological, algebraic and complex analytical methods, within the field of integrable systems, by addressing several theoretical and practical aspects. Contemporary integrability results, discovered in t... (Read more)

The study of ecological systems is often impeded by components that escape perfect observation, such as the trajectories of moving animals or the status of plant seed banks. These hidden components can be efficiently handled with statistical modeling by us... (Read more)

This book is part of Algebra and Geometry, a subject within the SCIENCES collection published by ISTE and Wiley, and the second of three volumes specifically focusing on algebra and its applications. Algebra and Applications 2 centers on the increasing rol... (Read more)

This book is entirely devoted to discrete time and provides a detailed introduction to the construction of the rigorous mathematical tools required for the evaluation of options in financial markets. Both theoretical and practical aspects are explored thro... (Read more)

Within the field of modeling complex objects in natural sciences, which considers systems that consist of a large number of interacting parts, a good tool for analyzing and fitting models is the theory of random evolutionary systems, considering their asym... (Read more)

From Euclidian to Hilbert Spaces analyzes the transition from finite dimensional Euclidian spaces to infinite-dimensional Hilbert spaces, a notion that can sometimes be difficult for non-specialists to grasp. The focus is on the parallels and differences b... (Read more)

The study of earthquakes is a multidisciplinary field, an amalgam of geodynamics, mathematics, engineering and more. The overriding commonality between them all is the presence of natural randomness. Stochastic studies (probability, stochastic processes... (Read more)

This book is part of Algebra and Geometry, a subject within the SCIENCES collection published by ISTE and Wiley, and the first of three volumes specifically focusing on algebra and its applications. Algebra and Applications 1 centers on non-associative alg... (Read more)

The aim of this book is to reflect the current cutting-edge thinking and established practices in the investigation of queueing systems and networks. This first volume includes ten chapters written by experts well-known in their areas. The book studies ... (Read more)

The aim of this book is to reflect the current cutting-edge thinking and established practices in the investigation of queueing systems and networks. This second volume includes eight chapters written by experts well-known in their areas. The book condu... (Read more)

This book provides easy access to the basic principles and methods for solving constrained and unconstrained convex optimization problems. Included are sections that cover: basic methods for solving constrained and unconstrained optimization problems with ... (Read more)

This book is the first of two volumes on random motions in Markov and semi-Markov random environments. This first volume focuses on homogenous random motions. This volume consists of two parts, the first describing the basic concepts and methods that ha... (Read more)

This book is the second of two volumes on random motions in Markov and semi-Markov random environments. This second volume focuses on high-dimensional random motions. This volume consists of two parts. The first expands many of the results found in Volu... (Read more)

This book analyzes stochastic evolutionary models under the impulse of diffusion, as well as Markov and semi-Markov switches. Models are investigated under the conditions of classical and non-classical (Levy and Poisson) approximations in addition to jumpi... (Read more)

This book is a collective volume authored by leading scientists in the field of stochastic modeling for dependent data, associated statistical topics and corresponding applications. These issues are crucial, as we face a growing need for increasingly compl... (Read more)

This book is the second of a set dedicated to the mathematical tools used in partial differential equations derived from physics. It presents the properties of continuous functions, which are useful for solving partial differential equations, and, more ... (Read more)

This book is devoted to the system analysis of statistical experiments, determined by the averaged sums of sampling random variables. The dynamics of statistical experiments are given by difference stochastic equations with a speci?ed regression function o... (Read more)

This book highlights mathematical research interests that appear in real life, such as the study and modeling of random and deterministic phenomena. As such, it provides current research in mathematics, with applications in biological and environmental sci... (Read more)

At the nexus of probability theory, geometry and statistics, a Gaussian measure is constructed on a Hilbert space in two ways: as a product measure and via a characteristic functional based on Minlos-Sazonov theorem. As such, it can be utilized for obtaini... (Read more)

Estimation of Stochastic Processes is intended for researchers in the field of econometrics, financial mathematics, statistics or signal processing. This book gives a deep understanding of spectral theory and estimation techniques for stochastic processes ... (Read more)

Published in three volumes, this series, Fundamentals of Advanced Mathematics, presents mathematical elements that make up the foundations of a number of contemporary scientific methods: modern systems theory, physics and engineering. This third volume ... (Read more)

This monograph studies the relationships between fractional Brownian motion (fBm) and other processes of more simple form. In particular, this book solves the problem of the projection of fBm onto the space of Gaussian martingales that can be represented a... (Read more)

This book analyzes stochastic processes on networks and regular structures such as lattices by employing the Markovian random walk approach. Part 1 is devoted to the study of local and non-local random walks. It shows how non-local random walk strategie... (Read more)

Earthquake occurrence modeling is a rapidly developing research area. This book deals with its critical issues, ranging from theoretical advances to practical applications. The introductory chapter outlines state-of-the-art earthquake modeling approache... (Read more)

This book presents an introduction to structural equation modeling (SEM) and facilitates the access of students and researchers in various scientific fields to this powerful statistical tool. It offers a didactic initiation to SEM as well as to the open-so... (Read more)

Piecewise-deterministic Markov processes form a class of stochastic models with a sizeable scope of applications: biology, insurance, neuroscience, networks, finance, etc. Such processes are defined by a deterministic motion punctuated by random jumps at r... (Read more)

This book on financial strategy covers the evolution of mergers and acquisitions by focusing primarily on value creation. Aware that the stages of this phenomenon remain largely misunderstood in finance, the author defines various types of operations, expl... (Read more)

This book reflects upon the current trends arising in both the theoretical study and the practical modeling of phenomena that exhibit fractionality. There is a tendency to transition from one type of fractionality to several types presented simultaneously;... (Read more)

This book explores the major impact of mathematical ideas on philosophical thought. It shows that from Antiquity (Plato) to the end of the Middle Ages (Nicholas of Cusa), philosophy and mathematics have been linked. At the time, visions of the world direct... (Read more)

The three volumes of this series of books, of which this is the second, put forward the mathematical elements that make up the foundations of a number of contemporary scientific methods: modern theory on systems, physics and engineering. Whereas the fi... (Read more)

Controlled branching (CB) processes constitute a very large class of stochastic processes, which includes different policies of immigration and emigration. The independence of individuals’ evolution is a fundamental assumption in the classical branching ... (Read more)

Finance and insurance companies are facing a wide range of parametric statistical problems. Statistical experiments generated by a sample of independent and identically distributed random variables are frequent and well understood, especially those consist... (Read more)

This book is concerned with the theory of stochastic processes and the theoretical aspects of statistics for stochastic processes. It combines classic topics such as construction of stochastic processes, associated filtrations, processes with independent i... (Read more)

Branching processes are stochastic processes which represent the reproduction of particles, such as individuals within a population, and thereby model demographic stochasticity. In branching processes in random environment (BPREs), additional environmental... (Read more)

This new edited volume consists of a collection of original articles written by leading industry experts in the area of factor investing. The chapters introduce readers to some of the latest research developments in the area of equity and alternative in... (Read more)

Portfolio diversification is widely practiced, but rarely discussed or challenged. Consequently, many investors end up disappointed, with portfolios that hold a little bit of everything but fail to be well diversified. This book introduces a new framew... (Read more)

This book constitutes an elementary introduction to rings and fields, in particular Galois rings and Galois fields, with regard to their application to the theory of quantum information, a field at the crossroads of quantum physics, discrete mathematics an... (Read more)

This book aims to promote regression methods for analyzing lifetime (or time-to-event) data that are based on a representation of the underlying process, and are therefore likely to offer greater scientific insight compared to purely empirical methods. ... (Read more)

Earthquake Occurrence provides the reader with a review of algorithms applicable for modeling seismicity, such as short-term earthquake clustering and pseudo-periodic long-term behavior of major earthquakes. The concept of the likelihood ratio of a set of ... (Read more)

The three volumes of this series of books, of which this is the first, put forward the mathematical elements that make up the foundations of a number of contemporary scientific methods: modern theory on systems, physics and engineering. This first volum... (Read more)

This book is devoted to the problems of construction and application of chi-squared goodness-of-fit tests for complete and censored data. Classical chi-squared tests assume that unknown distribution parameters are estimated using grouped data, but in pract... (Read more)

This book is the first of a set dedicated to the mathematical tools used in partial differential equations derived from physics. Its focus is on normed or semi-normed vector spaces, including the spaces of Banach, Fréchet and Hilbert, with new developmen... (Read more)

Credit risk is one of the most important contemporary problems for banks and insurance companies. Indeed, for banks, more than forty percent of the equities are necessary to cover this risk. Though this problem is studied by large rating agencies with sub... (Read more)

Exterior algebras have two key characteristics: they are relatively unknown and essential to linear algebra. Since being theorized by Grassmann in 1844, they have remained tragically forgotten. This book presents the construction and use of exterior alg... (Read more)

This book explores the quantitative steps of a financial investment process. The authors study how these steps are articulated in order to make any value creation, whatever the asset class, consistent and robust. The discussion includes factors, portfoli... (Read more)

This book considers various extensions of the topics treated in the first volume of this series, in relation to the class of models and the type of criterion for optimality. The regressors are supposed to belong to a generic finite dimensional Haar linear ... (Read more)

This book presents recent progress made in stochastic portfolio optimization with asymmetry information, modeled through different filtrations. The authors apply the theory of the enlargement of filtrations and solve the optimization problem. Two main ... (Read more)

This book confronts a growing business problem. How plausible is it for a business to control the dynamic of their capital? Central to this book is the theory of the probability of ruin and how this may not necessarily mean the end of business activity. In... (Read more)

Simulation has now become an integral part of research and development across many fields of study. Despite the large amounts of literature in the field of simulation and modeling, one recurring problem is the issue of accuracy and confidence level of cons... (Read more)

In April 2010 Europe was shocked by the Greek financial turmoil. At that time, the global financial crisis, which started in the summer of 2007 and reached systemic dimensions in September 2008 with the Lehman Brothers’ crash, took a new course. An adver... (Read more)

The book provides the mathematical basis for investigating numerical equations from physics, life sciences or engineering. Tools for analysis and algorithms are applied to a large set of relevant examples to show the difficulties and the limitations of the... (Read more)

The book is an original monograph on risk theory, which is traditionally considered a branch of insurance mathematics. It deals with different continuous-time risk models and mainly provides results obtained by the authors recently. The book covers seve... (Read more)

This book presents a short introduction to continuous-time financial models. An overview of the basics of stochastic analysis precedes a focus on the Black–Scholes and interest rate models. Other topics covered include self-financing strategies, option p... (Read more)

This book presents a new “factorized” formulation, for boundary value problems for linear elliptic partial differential equations. Based on the invariant embedding method of Richard Bellman, well-known for the synthesis of closed loop optimal control... (Read more)

This book is based on a lecture course to students specializing in the safety of technological processes and production. The author focuses on three main problems in technological risks and safety: elements of reliability theory, the basic notions, models... (Read more)

“Degradation process” refers to many types of reliability models, which correspond to various kinds of stochastic processes used for deterioration modeling. This book focuses on the case of a univariate degradation model with a continuous set of poss... (Read more)

Wireless networks represent an inexpensive and convenient way to connect to the Internet. However, despite their applications across several technologies, one challenge still remains: to understand the behavior of wireless sensor networks and assess their ... (Read more)

This book studies methods to concretely address inverse problems. An inverse problem arises when the causes that produced a given effect must be determined or when one seeks to indirectly estimate the parameters of a physical system. The author uses pract... (Read more)

This book is the first of a series which focuses on the interpolation and extrapolation of optimal designs, an area with significant applications in engineering, physics, chemistry and most experimental fields. In this volume, the authors emphasize the im... (Read more)

Devoted to financial markets both with discrete and continuous time, this book also describes how to make the transition from discrete to continuous time in option pricing. Chapter 1 presents the dynamic model of a financial market with discrete time. The ... (Read more)

Mark H.A. Davis introduced the Piecewise-Deterministic Markov Process (PDMP) class of stochastic hybrid models in an article in 1984. Today it is used to model a variety of complex systems in the fields of engineering, economics, management sciences, biolo... (Read more)

This book presents research work into the reliability of drinking water pipes. The infrastructure of water pipes is susceptible to routine failures, namely leakage or breakage, which occur in an aggregative manner in pipeline networks. Creating strategi... (Read more)

This book is a collection of exclusive new articles written by leading academics and practitioners in the area of risk-based and factor investing (RBFI). The articles introduce readers to some of the latest, cutting-edge research encountered by academics ... (Read more)

In 1994 and 1998 F. Delbaen and W. Schachermayer published two breakthrough papers in which they proved continuous-time versions of the Fundamental Theorem of Asset Pricing. This is one of the most remarkable achievements in modern Mathematical Finance, wh... (Read more)

Much of the previous literature on financial contagion and systematic risks has been motivated by the finding that cross-market correlations (resp. co-exceedances) between asset returns increase significantly during crisis periods. Is this increase due to ... (Read more)

In this book, the authors focus on two big families of stochastic processes: stochastic calculus, including Lévy processes, and Markov and semi-Markov models. From a financial point of view, essential concepts such as the Black and Scholes model, VaR indi... (Read more)

This book has been written for numerate non-specialists and serves three purposes. Firstly, it gathers together mathematical material from diverse but related fields of order statistics, records, extreme value theory, majorization, regular variation and... (Read more)

This book is devoted to integration, one of the two main operations in calculus. In Part 1, the definition of the integral of a one-variable function is different (not essentially, but rather methodically) from traditional definitions of Riemann or Leb... (Read more)

This updated and revised 2nd edition of the three-volume Combinatorial Optimization series covers a very large set of topics in this area, dealing with fundamental notions and approaches as well as several classical applications of Combinatorial Optimizati... (Read more)

This updated and revised 2nd edition of the three-volume Combinatorial Optimization series covers a very large set of topics in this area, dealing with fundamental notions and approaches as well as several classical applications of Combinatorial Optimizati... (Read more)

This updated and revised 2nd edition of the three-volume Combinatorial Optimization series covers a very large set of topics in this area, dealing with fundamental notions and approaches as well as several classical applications of Combinatorial Optimizati... (Read more)

Statistical Models and Methods for Reliability and Survival Analysis brings together contributions by specialists in statistical theory as they discuss their applications providing up-to-date developments in methods used in survival analysis, statistical g... (Read more)

Markov chains are a fundamental class of stochastic processes. They are widely used to solve problems in a large number of domains such as operational research, computer science, communication networks and manufacturing systems. The success of Markov chain... (Read more)

The aim of this book is to promote interaction between engineering, finance and insurance, as these three domains have many models and methods of solution in common for solving real-life problems. The authors point out the strict inter-relations that exist... (Read more)

The family of statistical models known as Rasch models started with a simple model for responses to questions in educational tests presented together with a number of related models that the Danish mathematician Georg Rasch referred to as models for measur... (Read more)

Generally, books on mathematical statistics are restricted to the case of independent identically distributed random variables. In this book however, both this case AND the case of dependent variables, i.e. statistics for discrete and continuous time proce... (Read more)

This book addresses the stochastic modeling of telecommunication networks, introducing the main mathematical tools for that purpose, such as Markov processes, real and spatial point processes and stochastic recursions, and presenting a wide list of results... (Read more)

The book will present all the stochastic models that can be used for the study of pension schemes and the management of pension funds. Advanced stochastic tools will be used for the construction of the models presented. Quantitative finance has become a... (Read more)

The publication of the first book by Kenneth Arrow and Hervé Raynaud, in 1986, led to an important wave of research in the field of axiomatic approach applied to managerial logic. Managerial Logic summarizes the prospective results of this research and of... (Read more)

This is an introduction to stochastic integration and stochastic differential equations written in an understandable way for a wide audience, from students of mathematics to practitioners in biology, chemistry, physics, and finances. The presentation is b... (Read more)

Statistical analysis of data sets usually involves construction of a statistical model of the distribution of data within the available sample – and by extension the distribution of all data of the same category in the world. Statistical models are eith... (Read more)

Statistical analysis of data sets usually involves construction of a statistical model of the distribution of data within the available sample – and by extension the distribution of all data of the same category in the world. Statistical models are eith... (Read more)

This book provides a pedagogical examination of the way in which stochastic models are encountered in applied sciences and techniques such as physics, engineering, biology and genetics, economics and social sciences. It covers Markov and semi-Markov models... (Read more)

Stochastic finance and financial engineering are fields of science that have expanded rapidly over the past four decades, due mainly to the success of sophisticated quantitative methodologies in helping professionals manage financial risks. In recent years... (Read more)

These two volumes provide a foundation course on applied stochastic finance for students, financial analysts and practitioners, and any professional interested in learning advanced mathematical and stochastic methods through finance. The books are illus... (Read more)

This textbook covers the uniform laws of financial practice and classical methods for evaluating amortization, annuities, capital markets, interest rates, liability, sinking funds and term structures. An overview of stochastic processes and the Itô calcu... (Read more)

This book offers comprehensive coverage of the basic mathematical tools for the engineer in the field of communication technologies – generation, processing and transport of all forms of information, data and images. It provides the essential results in ... (Read more)

The book is devoted to developing the asymptotic theory for the class of switching queueing models which covers state-dependent models in a Markov or semi-Markov environment, models under the influence of flows of external or internal perturbations, unreli... (Read more)

Reliability and survival analysis are important applications of stochastic mathematics (probability, statistics and stochastic processes) that are usually covered separately in spite of the similarity of the mathematical theory involved. This book aims ... (Read more)

This book considers the special class of random processes known as semi-Markov processes. These possess the Markov property with respect to any intrinsic Markov time such as the first exit time from an open set or a finite iteration of these times. This... (Read more)

This is the first book devoted entirely to Particle Swarm Optimization (PSO), which is a non-specific algorithm, similar to evolutionary algorithms, such as taboo search and ant colonies. Since its original development in 1995, PSO has mainly been applied ... (Read more)