Essentials of Stochastic Processes / Edition 1 by Richard Durrett, R. Durrett, Rick Durrett | | 9780387988368 | Hardcover | Barnes & Noble
Essentials of Stochastic Processes / Edition 1

Essentials of Stochastic Processes / Edition 1

by Richard Durrett, R. Durrett, Rick Durrett
     
 

ISBN-10: 038798836X

ISBN-13: 9780387988368

Pub. Date: 07/30/1999

Publisher: Springer-Verlag New York, LLC

Overview

To follow.

Product Details

ISBN-13:
9780387988368
Publisher:
Springer-Verlag New York, LLC
Publication date:
07/30/1999
Series:
Springer Texts in Statistics Series
Edition description:
1st ed. 1999. Corr. 2nd printing
Pages:
289
Product dimensions:
9.21(w) x 6.14(h) x 0.69(d)

Related Subjects

Table of Contents

Review of Probability
--Probabilities, Independence
--Random Variables, Distributions
--Expected Value, Moments

1   Markov Chains
--Definitions and Examples
--Multi-step Transition Probabilities
--Classification of States
--Limit Behavior
--Some Special Examples
--One Step Calculations
--Infinite State Spaces
--Proofs of Convergence Theorems
--Exercises

2   Martingales
--Conditional Expectation
--Examples of Martingales
--Optional Stopping Theorem
--Applications
--Exercises

3   Poisson Processes
--Exponential Distribution
--Defining the Poisson Process
--Compund Poisson Processes
--Thinning and Superposition
--Conditioning
--Spatial Poisson Processes
--Exercises

4   Continuous-time Markov Chains
--Definitions and Examples
--Computing the Transition Probability
--Limiting Behavior
--Queueing Chains
--Reversibility
--Queueing Networks
--Closed Queueing Networks
--Exercises

5   Renewal Theory
--Basic Definitions
--Laws of Large Numbers
--Applications to Queueing Theory
--Age and Residual Life
--Exercises

6   Brownian Motion
--Basic Definitions
--Markov Property, Reflection Principle
--Martingales, Hitting Times
--Option Pricing in Discrete Time
--The Black-Scholes Formula
--Exercises

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