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 Rosenthal, Jeffrey S. (Jeffrey Seth)
 2nd ed  Singapore ; Hackensack, N.J. : World Scientific, ©2006
 Description
 Book — 1 online resource (xvi, 219 pages) : illustrations
 Summary

 The need for measure theory
 Probability triples
 Further probabilistic foundations
 Expected values
 Inequalities and convergence
 Distributions of random variables
 Stochastic processes and gambling games
 Discrete Markov chains
 More probability theorems
 Weak convergence
 Characteristic functions
 Decomposition of probability laws
 Conditional probability and expectation
 Martingales
 General stochastic processes
 Mathematical background
 Online

 ProQuest Ebook Central Access limited to 3 simultaneous users
 Google Books (Full view)
MATH13601
 Course
 MATH13601  Stochastic Processes
 Instructor(s)
 Dembo, Amir
2. Introduction to stochastic processes [2006]
 Lawler, Gregory F., 1955
 2nd ed  Boca Raton : Chapman & Hall/CRC, 2006
 Description
 Book — 1 online resource (xiii, 234 pages)
 Summary

 Preface to Second Edition Preface to First Edition PRELIMINARIES Introduction Linear Differential Equations Linear Difference Equations Exercises FINITE MARKOV CHAINS Definitions and Examples LargeTime Behavior and Invariant Probability Classification of States Return Times Transient States Examples Exercises COUNTABLE MARKOV CHAINS Introduction Recurrence and Transience Positive Recurrence and Null Recurrence Branching Process Exercises CONTINUOUSTIME MARKOV CHAINS Poisson Process Finite State Space BirthandDeath 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 if Ito's Formula Continuous Martingales Girsanov Transformation FeynmanKac Formula BlackScholes Formula Simulation Exercises Suggestions for Further Reading Index.
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 Online

 ProQuest Ebook Central Access limited to 3 simultaneous users
 Google Books (Full view)
MATH13601
 Course
 MATH13601  Stochastic Processes
 Instructor(s)
 Dembo, Amir