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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
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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.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Online

 ProQuest Ebook Central Access limited to 3 simultaneous users
 Google Books (Full view)
MATH13601
 Course
 MATH13601  Stochastic Processes
 Instructor(s)
 Dembo, Amir
3. Stochastic calculus for finance [2004  ]
 Shreve, Steven E.
 New York : Springer, c2004
 Description
 Book — v. : ill. ; 25 cm.
 Summary

 v. 1. The binomial asset pricing model
 v. 2. Continuoustime models.
(source: Nielsen Book Data)
This book evolved from the first ten years of the Carnegie Mellon professional Master's program in Computational Finance. The contents of the book have been used successfully with students whose mathematics background consists of calculus and calculusbased probability. The text gives both precise statements of results, plausibility arguments, and even some proofs. But more importantly, intuitive explanations, developed and refined through classroom experience with this material, are provided throughout the book. Volume I introduces the fundamental concepts in a discretetime setting and Volume II builds on this foundation to develop stochastic calculus, martingales, riskneutral pricing, exotic options, and term structure models, all in continuous time. The book includes a selfcontained treatment of the probability theory needed for stochastic calculus, including Brownian motion and its properties. Advanced topics include foreign exchange models, forward measures, and jumpdiffusion processes. Classroomtested exercises conclude every chapter; some of these extend the theory while others are drawn from practical problems in quantitative finance. Instructor's manual available.
(source: Nielsen Book Data)
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MATH13601
 Course
 MATH13601  Stochastic Processes
 Instructor(s)
 Dembo, Amir
4. A first course in stochastic processes [1975]
 Karlin, Samuel, 19232007, author.
 Second edition.  New York : Academic Press, [1975]
 Description
 Book — 1 online resource (xvi, 557 pages) : illustrations
 Summary

 Preface. Elements of Stochastic Processes. Markov Chains. The Basic Limit Theorem of Markov Chains and Applications. Classical Examples of Continuous Time Markov Chains. Renewal Processes. Martingales. Brownian Motion. Branching Processes. Stationary Processes. Review of Matrix Analysis. Index.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
MATH13601
 Course
 MATH13601  Stochastic Processes
 Instructor(s)
 Dembo, Amir