Stirzaker David. Stochastic Processes and Models

First published 2005.
Contents.
Probability.
Conditional probability and independence.
Random variables.
Random vectors.
Transformations of random variables.
Expectation and moments.
Conditioning.
Generating functions.
Multivariate normal.
Introduction to stochastic processes.
Preamble.
Essential examples; random walks.
The long run.
Martingales.
Poisson processes.
Renewals.
Branching processes.
Miscellaneous models.
Some technical details.
Markov chains.
The Markov property; examples.
Structure and n-step probabilities.
First-step analysis and hitting times.
The Markov property revisited.
Classes and decomposition.
Stationary distribution: the long run.
Reversible chains.
Markov chains in continuous time.
Introduction and examples.
Forward and backward equations.
Birth processes: explosions and minimality.
Recurrence and transience.
Hitting and visiting.
Stationary distributions and the long run.
Reversibility.
Queues.
Miscellaneous models.
Diffusions.
Introduction: Brownian motion.
The Wiener process.
Reflection principle; first-passage times.
Functions of diffusions.
Martingale methods.
Stochastic calculus: introduction.
The stochastic integral.
Itф’s formula.
Processes in space.
Hints and solutions for starred exercises and problems.
Further reading.
Index.