Introduction to Stochastic Processes

ISBN-10: 0486497976

ISBN-13: 9780486497976

Edition: 2013

Authors: Erhan Cinlar

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Description:

This clear presentation of the most fundamental models of random phenomena employs methods that recognize computer-related aspects of theory. Topics include probability spaces and random variables, expectations and independence, Bernoulli processes and sums of independent random variables, Poisson processes, Markov chains and processes, and renewal theory. Includes an introduction to basic stochastic processes. 1975 edition.
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Book details

List price: $36.50
Copyright year: 2013
Publisher: Dover Publications, Incorporated
Publication date: 2/20/2013
Binding: Paperback
Pages: 416
Size: 6.00" wide x 9.00" long x 0.80" tall
Weight: 1.188
Language: English

Preface
Probability Spaces and Random Variables
Probability Spaces
Random Variables and Stochastic Processes
Conditional Probability
Exercises
Expectations and Independence
Expected Value
Conditional Expectations
Exercises
Bernoulli Processes and Sums of Independent Random Variables
Bernoulli Process
Numbers of Successes
Times of Successes
Sums of Independent Random Variables
Exercises
Poisson Processes
Arrival Counting Process
Times of Arrivals
Forward Recurrence Times
Superposition of Poisson Processes
Decomposition of Poisson Processes
Compound Poisson Processes
Non-stationary Poisson Processes
Exercises
Markov Chains
Introduction
Visits to a Fixed State
Classification of States
Exercises
Limiting Behavior and Applications of Markov Chains
Computation of R and F
Recurrent States and the Limiting Probabilities
Periodic States
Transient States
Applications to Queueing Theory: M/G/l Queue
Queueing System G/M/l
Branching Processes
Exercises
Potentials, Excessive Functions, and Optimal Stopping of Markov Chains
Potentials
Excessive Functions
Optimal Stopping
Games with Discounting and Fees
Exercises
Markov Processes
Markov Processes
Sample Path Behavior
Structure of a Markov Process
Potentials and Generators
Limit Theorems
Birth and Death Processes
Exercises
Renewal Theory
Renewal Processes
Regenerative Processes and Renewal Theory
Delayed and Stationary Processes
Exercises
Markov Renewal Theory
Markov Renewal Processes
Markov Renewal Functions and Classification of States
Markov Renewal Equations
Limit Theorems
Semi-Markov Processes
Semi-Regenerative Processes
Applications to Queueing Theory
Exercises
Afterword
Appendix. Non-Negative Matrices
Eigenvalues and Eigenvectors
Spectral Representations
Positive Matrices
Non-Negative Matrices
Limits and Rates of Convergence
References
Answers to Selected Exercises
Index of Notations
Subject Index
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