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Stochastic processes : from applications to theory

Del Moral, Pierre, author.

Stochastic processes : from applications to theory

Del Moral, Pierre, author.

9781315381619

9781315321257

First edition.

1 online resource (916 pages)

part I An illustrated guide -- chapter 1 Motivating examples -- chapter 2 Selected topics -- chapter 3 Computational and theoretical aspects -- part II Stochastic simulation -- chapter 4 Simulation toolbox -- chapter 5 Monte Carlo integration -- chapter 6 Some illustrations -- part III Discrete time processes -- chapter 7 Markov chains -- chapter 8 Analysis toolbox -- chapter 9 Computational toolbox -- part IV Continuous time processes -- chapter 10 Poisson processes -- chapter 11 Markov chain embeddings -- chapter 12 Jump processes -- chapter 13 Piecewise deterministic processes -- chapter 14 Diffusion processes -- chapter 15 Jump diffusion processes -- chapter 16 Nonlinear jump diffusion processes -- chapter 17 Stochastic analysis toolbox -- chapter 18 Path space measures -- part V Processes on manifolds -- chapter 19 A review of differential geometry -- chapter 20 Stochastic differential calculus on manifolds -- chapter 21 Parametrizations and charts -- chapter 22 Stochastic calculus in chart spaces -- chapter 23 Some analytical aspects -- chapter 24 Some illustrations -- part VI Some application areas -- chapter 25 Simple random walks -- chapter 26 Iterated random functions -- chapter 27 Computational and statistical physics -- chapter 28 Dynamic population models -- chapter 29 Gambling, ranking and control -- chapter 30 Mathematical finance.

Unlike traditional books presenting stochastic processes in an academic way, this book includes concrete applications that students will find interesting such as gambling, finance, physics, signal processing, statistics, fractals, and biology. Written with an important illustrated guide in the beginning, it contains many illustrations, photos and pictures, along with several website links. Computational tools such as simulation and Monte Carlo methods are included as well as complete toolboxes for both traditional and new computational techniques.

Stochastic models.

Stochastic processes.

Penev, Spiridon, 1955-

CRC Press.

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