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.

Table of Contents

I: An illustrated guide

1 Motivating examples

2 Selected topics

3 Computational and theoretical aspects

II: Stochastic simulation

4 Simulation toolbox

5 Monte Carlo integration

6 Some illustrations

Ill: Discrete time processes

7 Markov chains

8 Analysis toolbox

9 Computational toolbox

IV: Continuous time processes

10 Poisson processes

11 Markov chain embeddings

12 Jump processes

13 Piecewise deterministic processes

14 Diffusion processes

15 Jump diffusion processes

16 Nonlinear jump diffusion processes

17 Stochastic analysis toolbox

18 Path space measures

V: Processes on manifolds

19 A review of differential geometry

20 Stochastic differential calculus on manifolds

21 Parametrizations and charts

22 Stochastic calculus in chart spaces

23 Some analytical aspects

24 Some illustrations

VI: Some application areas

25 Simple random walks

26 Iterated random functions

27 Computational and statistical physics

28 Dynamic population models

29 Gambling, ranking and control

30 Mathematical finance

About the Authors

Pierre Del Moral and Spiridon Penev are professors in the School of Mathematics and Statistics at the University of New South Wales.