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 random times, and offer simple yet challenging models to study. Nevertheless, the issue of statistical estimation of the parameters ruling the jump mechanism is far from trivial.
Responding to new developments in the field as well as to current research interests and needs, Statistical Inference for Piecewise-deterministic Markov Processes offers a detailed and comprehensive survey of state-of-the-art results. It covers a wide range of general processes as well as applied models. The book also focuses on statistics in the context of Markov chains, since piecewise-deterministic Markov processes are characterized by an embedded Markov chain corresponding to the position of the process right after the jumps.
1. Statistical Analysis for Structured Models on Trees, Marc Hoffmann and Adélaïde Olivier.
2. Regularity of the Invariant Measure and Non-parametric Estimation of the Jump Rate, Pierre Hodara, Nathalie Krell and Eva Löcherbach.
3. Level Crossings and Absorption of an Insurance Model, Romain Azaïs and Alexandre Genadot.
4. Robust Estimation for Markov Chains with Applications to Piecewise-deterministic Markov Processes, Patrice Bertail, Gabriela Ciolek and Charles Tillier.
5. Numerical Method for Control of Piecewise-deterministic Markov Processes, Benoîte de Saporta and François Dufour.
6. Rupture Detection in Fatigue Crack Propagation, Romain Azaïs, Anne Gégout-Petit and Florine Greciet.
7. Piecewise-deterministic Markov Processes for Spatio-temporal Population Dynamics, Candy Abboud, Rachid Senoussi and Samuel Soubeyrand.
Romain Azaïs is a researcher in applied mathematics. He completed his PhD thesis on nonparametric statistics for piecewise-deterministic Markov processes in Bordeaux in 2013. After a postdoctoral position in Montpellier, he obtained a permanent research position at Inria Nancy. He moved to ENS Lyon in 2018.
Florian Bouguet is currently a CPGE teaching professor of mathematics in China. He completed his PhD thesis on piecewise-deterministic Markov models at Rennes University, France, in 2016.
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