Description
This textbook introduces the theory of stochastic processes, that is, randomness which proceeds in time. Using concrete examples like repeated gambling and jumping frogs, it presents fundamental mathematical results through simple, clear, logical theorems and examples. It covers in detail such essential material as Markov chain recurrence criteria, the Markov chain convergence theorem, and optional stopping theorems for martingales. The final chapter provides a brief introduction to Brownian motion, Markov processes in continuous time and space, Poisson processes, and renewal theory.
Interspersed throughout are applications to such topics as gambler's ruin probabilities, random walks on graphs, sequence waiting times, branching processes, stock option pricing, and Markov Chain Monte Carlo (MCMC) algorithms.
The focus is always on making the theory as well-motivated and accessible as possible, to allow students and readers to learn this fascinating subject as easily and painlessly as possible.
Author: Jeffrey S. Rosenthal
Publisher: World Scientific Publishing Company
Published: 10/04/2019
Pages: 212
Binding Type: Paperback
Weight: 0.64lbs
Size: 9.00h x 6.00w x 0.45d
ISBN13: 9789811208973
ISBN10: 9811208972
BISAC Categories:
- Mathematics | Probability & Statistics | Stochastic Processes
- Mathematics | Probability & Statistics | Regression Analysis