9781584886518

Introduction to Stochastic Processes, Second Edition

by ;
  • ISBN13:

    9781584886518

  • ISBN10:

    158488651X

  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 5/16/2006
  • Publisher: Chapman & Hall/

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

Purchase Benefits

  • Free Shipping On Orders Over $59!
    Your order must be $59 or more to qualify for free economy shipping. Bulk sales, PO's, Marketplace items, eBooks and apparel do not qualify for this offer.
  • Get Rewarded for Ordering Your Textbooks! Enroll Now
  • We Buy This Book Back!
    In-Store Credit: $15.75
    Check/Direct Deposit: $15.00
List Price: $99.95 Save up to $39.98
  • Rent Book $59.97
    Add to Cart Free Shipping

    TERM
    PRICE
    DUE

Supplemental Materials

What is included with this book?

  • The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.
  • The Rental copy of this book is not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

Summary

Emphasizing fundamental mathematical ideas rather than proofs, Introduction to Stochastic Processes, Second Edition provides quick access to important foundations of probability theory applicable to problems in many fields. Assuming that you have a reasonable level of computer literacy, the ability to write simple programs, and the access to software for linear algebra computations, the author approaches the problems and theorems with a focus on stochastic processes evolving with time, rather than a particular emphasis on measure theory.For those lacking in exposure to linear differential and difference equations, the author begins with a brief introduction to these concepts. He proceeds to discuss Markov chains, optimal stopping, martingales, and Brownian motion. The book concludes with a chapter on stochastic integration. The author supplies many basic, general examples and provides exercises at the end of each chapter.New to the Second Edition:· Expanded chapter on stochastic integration that introduces modern mathematical finance· Introduction of Girsanov transformation and the Feynman-Kac formula· Expanded discussion of Itô's formula and the Black-Scholes formula for pricing options· New topics such as Doob's maximal inequality and a discussion on self similarity in the chapter on Brownian motionApplicable to the fields of mathematics, statistics, and engineering as well as computer science, economics, business, biological science, psychology, and engineering, this concise introduction is an excellent resource both for students and professionals.

Table of Contents

Preface to Second Edition ix
Preface to First Edition xi
Preliminaries
1(8)
Introduction
1(1)
Linear Differential Equations
1(2)
Linear Difference Equations
3(3)
Exercises
6(3)
Finite Markov Chains
9(34)
Definitions and Examples
9(5)
Large-Time Behavior and Invariant Probability
14(3)
Classification of States
17(7)
Reducibility
19(2)
Periodicity
21(1)
Irreducible, aperiodic chains
22(1)
Reducible or periodic chains
22(2)
Return Times
24(2)
Transient States
26(5)
Examples
31(4)
Exercises
35(8)
Countable Markov Chains
43(22)
Introduction
43(2)
Recurrence and Transience
45(5)
Positive Recurrence and Null Recurrence
50(3)
Branching Process
53(4)
Exercises
57(8)
Continuous-Time Markov Chains
65(22)
Poisson Process
65(3)
Finite State Space
68(6)
Birth-and-Death Processes
74(7)
General Case
81(1)
Exercises
82(5)
Optimal Stopping
87(14)
Optimal Stopping of Markov Chains
87(6)
Optimal Stopping with Cost
93(3)
Optimal Stopping with Discounting
96(2)
Exercises
98(3)
Martingales
101(30)
Conditional Expectation
101(5)
Definition and Examples
106(4)
Optional Sampling Theorem
110(4)
Uniform Integrability
114(2)
Martingale Convergence Theorem
116(6)
Maximal Inequalities
122(3)
Exercises
125(6)
Renewal Processes
131(24)
Introduction
131(5)
Renewal Equation
136(8)
Discrete Renewal Processes
144(4)
M/G/1 and G/M/1 Queues
148(3)
Exercises
151(4)
Reversible Markov Chains
155(18)
Reversible Processes
155(2)
Convergence to Equilibrium
157(5)
Markov Chain Algorithms
162(4)
A Criterion for Recurrence
166(4)
Exercises
170(3)
Brownian Motion
173(26)
Introduction
173(3)
Markov Property
176(5)
Zero Set of Brownian Motion
181(3)
Brownian Motion in Several Dimensions
184(5)
Recurrence and Transience
189(2)
Fractal Nature of Brownian Motion
191(1)
Scaling Rules
192(1)
Brownian Motion with Drift
193(2)
Exercises
195(4)
Stochastic Integration
199(32)
Integration with Respect to Random Walk
199(1)
Integration with Respect to Brownian Motion
200(5)
Ito's Formula
205(4)
Extensions of Ito's Formula
209(7)
Continuous Martingales
216(2)
Girsanov Transformation
218(3)
Feynman-Kac Formula
221(2)
Black-Scholes Formula
223(5)
Simulation
228(1)
Exercises
228(3)
Suggestions for Further Reading 231(2)
Index 233

Rewards Program

Write a Review