# Applied Stochastic Processes

₹495.00

- Publisher: CRC PRESS
- ISBN-13: 9781466589339
- Pages: 208
- Binding: Paperback
- Year of Pub / Reprint Year: 2015

## Description

**About The Book**

Applied Stochastic Processes presents a concise, graduate-level treatment of the subject, emphasizing applications and practical computation. It also establishes the complete mathematical theory in an accessible way.

After reviewing basic probability, the text covers Poisson processes, renewal processes, discrete- and continuous-time Markov chains, and Brownian motion. It also offers an introduction to stochastic differential equations. While the main applications described are queues, the book also considers other examples, such as the mathematical model of a single stock market.

With exercises in most sections, this book provides a clear, practical introduction for beginning graduate students. The material is presented in a straightforward manner using short, motivating examples. In addition, the author develops the mathematical theory with a strong emphasis on probability intuition.

Table of Contents

Probability and Stochastic Processes

Probability

Random variables and their distributions

Mathematical expectation

Joint distribution and independence

Convergence of random variables

Laplace transform and generating functions

Examples of discrete distributions

Examples of continuous distributions

Stochastic processes

Stopping times

Conditional expectation

Poisson Processes

Introduction to Poisson processes

Arrival and inter-arrival times of Poisson processes

Conditional distribution of arrival times

Poisson processes with different types of events

Compound Poisson processes

Nonhomogeneous Poisson processes

Renewal Processes

An introduction to renewal processes

Renewal reward processes

Queuing systems

Queue lengths, waiting times, and busy periods

Renewal equation

Key renewal theorem

Regenerative processes

Queue length distribution and PASTA

Discrete Time Markov Chains

Markov property and transition probabilities

Examples of discrete time Markov chains

Multi-step transition and reaching probabilities

Classes, recurrence, and transience

Periodicity, class property, and positive recurrence

Expected hitting time and hitting probability

Stationary distribution

Limiting properties

Continuous Time Markov Chain

Markov property and transition probability

Transition rates

Stationary distribution and limiting properties

Birth and death processes

Exponential queuing systems

Time reversibility

Hitting time and phase-type distributions

Queuing systems with time-varying rates

Brownian Motion and Beyond

Brownian motion

Standard Brownian motion and its maximum

Conditional expectation and martingales

Brownian motion with drift

Stochastic integrals

Itô’s formula and stochastic differential equations

A single stock market model

Bibliography

Index

Features

Offers a succinct, accessible account of applied stochastic processes for a first-year graduate course

Provides systematic coverage of queuing applications, unlike similar texts on stochastic processes

Includes an introduction to stochastic differential equations

Contains exercises at the end of most sections and a brief bibliography at the back of the book

Solutions manual and figure slides available upon qualifying course adoption

**About The Author**

Ming Liao is a professor in the Department of Mathematics and Statistics at Auburn University. He has published 45 research papers and one monograph on probability theory. He received a Ph.D. from Stanford University.