Committee login






Small thumbnail

Secure Connected Objects

Small thumbnail

Banach, Fréchet, Hilbert and Neumann Spaces

Analysis for PDEs Set Volume 1

Small thumbnail

Semi-Markov Migration Models for Credit Risk

Stochastic Models for Insurance Set Volume 1

Small thumbnail

Human Exposure to Electromagnetic Fields

From Extremely Low Frequency (ELF) to Radio Frequency

Small thumbnail

Enterprise Interoperability


Small thumbnail

Data Treatment in Environmental Sciences

Multivaried Approach

Small thumbnail

From Pinch Methodology to Pinch-Exergy Integration of Flexible Systems

Thermodynamics Energy, Environment, Economy Set

Small thumbnail

Exterior Algebras

Elementary Tribute to Grassmann's Ideas

Small thumbnail

Nonlinear Theory of Elastic Plates

Small thumbnail

Cognitive Approach to Natural Language Processing

Small thumbnail

Branching Random Walks in Non-homogeneous Environments

Elena Yarovaya, Faculty of Mechanics and Mathematics, Moscow, Russia

ISBN: 9781848212084

  Hardback   288 pp.

100 USD

Add to cart




The book is devoted to a modern section of the probability theory, the so-called theory of branching random walks.
Chapter 1 describes the random walk model in the finite branching one-source environment.
Chapter 2 is devoted to a model of homogeneous, symmetrical, irreducible random walk (without branching) with finite variance of the jumps on the multidimensional integer continuous-time lattice where transition is possible to an arbitrary point of the lattice and not only to the neighbor state. This model is a generalization of the simple symmetrical random walk often encountered in the applied studies.
In Chapter 3 the branching random walk is studied by means of the spectral methods. Here, the property of monotonicity of the mean number of particles in the source plays an important role in the subsequent parts of the book.
Chapter 4 demonstrates that existence of an isolated positive eigenvalue in the spectrum of random walk generator defines the exponential growth of the process in the supercritical case.
Chapter 5 exemplifies application of the Tauberian theorems in the asymptotical problems of the probability theory.
Finaly Chapters 6 and 7 are devoted to a detailed examination of survival probabilities in the critical and subcritical cases.


1. Model Description and Basic Equations.
2. Random Walk without branching.
3. Spectral Classification of the First Moments.
4. Limit Theorem for the Supercritical Case.
5. Moments in the Critical and Subcritical Cases.
6. Limit Theorems for the Critical Case.
7. Limit Theorems for the Subcritical Case.

Related Titles

0.03326 s.