Introduction to Stochastic Processes

Name: Introduction to Stochastic Processes
Price: 18.41 USD
Availability: InStock
ISBN: 9780486497976

ISBN-10: 0486497976

ISBN-13: 9780486497976

Edition: 2013

Authors: Erhan Cinlar

List price: $36.50

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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.

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: 1.386
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