ABSTRACT

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.

part I|68 pages

An illustrated guide

chapter 1|22 pages

Motivating examples

chapter 2|18 pages

Selected topics

chapter 3|28 pages

Computational and theoretical aspects

part II|50 pages

Stochastic simulation

chapter 4|28 pages

Simulation toolbox

chapter 5|8 pages

Monte Carlo integration

chapter 6|14 pages

Some illustrations

part III|178 pages

Discrete time processes

chapter 7|20 pages

Markov chains

chapter 8|80 pages

Analysis toolbox

chapter 9|78 pages

Computational toolbox

part IV|236 pages

Continuous time processes

chapter 10|14 pages

Poisson processes

chapter 11|24 pages

Markov chain embeddings

chapter 12|26 pages

Jump processes

chapter 13|30 pages

Piecewise deterministic processes

chapter 14|32 pages

Diffusion processes

chapter 15|38 pages

Jump diffusion processes

chapter 16|18 pages

Nonlinear jump diffusion processes

chapter 17|20 pages

Stochastic analysis toolbox

chapter 18|34 pages

Path space measures

part V|158 pages

Processes on manifolds

chapter 19|44 pages

A review of differential geometry

chapter 21|36 pages

Parametrizations and charts

chapter 22|36 pages

Stochastic calculus in chart spaces

chapter 23|10 pages

Some analytical aspects

chapter 24|34 pages

Some illustrations

part VI|148 pages

Some application areas

chapter 25|20 pages

Simple random walks

chapter 26|12 pages

Iterated random functions

chapter 27|26 pages

Computational and statistical physics

chapter 28|28 pages

Dynamic population models

chapter 29|28 pages

Gambling, ranking and control

chapter 30|34 pages

Mathematical finance