Introduction to Stochastic Processes

Name: Introduction to Stochastic Processes
Availability: InStock
ISBN: 9781584886518

ISBN-10: 158488651X

ISBN-13: 9781584886518

Edition: 2nd 2006 (Revised)

Authors: Gregory F. Lawler

List price: $115.00

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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…

Book details

List price: $115.00
Edition: 2nd
Copyright year: 2006
Publisher: CRC Press LLC
Publication date: 5/16/2006
Binding: Hardcover
Pages: 248
Size: 6.38" wide x 9.45" long x 0.71" tall
Weight: 1.276



Preface to Second Edition


Preface to First Edition



Preliminaries



Introduction



Linear Differential Equations



Linear Difference Equations



Exercises



Finite Markov Chains



Definitions and Examples



Large-Time Behavior and Invariant Probability



Classification of States



Reducibility



Periodicity



Irreducible, aperiodic chains



Reducible or periodic chains



Return Times



Transient States



Examples



Exercises



Countable Markov Chains



Introduction



Recurrence and Transience



Positive Recurrence and Null Recurrence



Branching Process



Exercises



Continuous-Time Markov Chains



Poisson Process



Finite State Space



Birth-and-Death Processes



General Case



Exercises



Optimal Stopping



Optimal Stopping of Markov Chains



Optimal Stopping with Cost



Optimal Stopping with Discounting



Exercises



Martingales



Conditional Expectation



Definition and Examples



Optional Sampling Theorem



Uniform Integrability



Martingale Convergence Theorem



Maximal Inequalities



Exercises



Renewal Processes



Introduction



Renewal Equation



Discrete Renewal Processes



M/G/1 and G/M/1 Queues



Exercises



Reversible Markov Chains



Reversible Processes



Convergence to Equilibrium



Markov Chain Algorithms



A Criterion for Recurrence



Exercises



Brownian Motion



Introduction



Markov Property



Zero Set of Brownian Motion



Brownian Motion in Several Dimensions



Recurrence and Transience



Fractal Nature of Brownian Motion



Scaling Rules



Brownian Motion with Drift



Exercises



Stochastic Integration



Integration with Respect to Random Walk



Integration with Respect to Brownian Motion



Ito's Formula



Extensions of Ito's Formula



Continuous Martingales



Girsanov Transformation



Feynman-Kac Formula



Black-Scholes Formula



Simulation



Exercises


Suggestions for Further Reading


Index