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 Rosenthal, Jeffrey S. (Jeffrey Seth)
 2nd ed.  Hackensack, N.J. : World Scientific, c2006.
 Description
 Book — xvi, 219 p. : ill. ; 23 cm.
 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.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA273 .R784 2006  Unknown On reserve at Li and Ma Science Library 2day loan 
MATH13601, STATS21901
 Course
 MATH13601  Stochastic Processes
 Instructor(s)
 Dembo, Amir
 Course
 STATS21901  Stochastic Processes
 Instructor(s)
 He, Jimmy
2. Introduction to stochastic processes [2006]
 Lawler, Gregory F., 1955
 2nd ed.  Boca Raton : Chapman & Hall/CRC, 2006.
 Description
 Book — xiii, 234 p. : ill. ; 25 cm.
 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
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA274 .L38 2006  Unknown On reserve at Li and Ma Science Library 2day loan 
MATH13601, STATS21901
 Course
 MATH13601  Stochastic Processes
 Instructor(s)
 Dembo, Amir
 Course
 STATS21901  Stochastic Processes
 Instructor(s)
 He, Jimmy
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)
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks


HG106 .S57 2004 V.1  Unknown 
HG106 .S57 2004 V.2  Unknown On reserve at Li and Ma Science Library 2day loan 
MATH13601, STATS21901
 Course
 MATH13601  Stochastic Processes
 Instructor(s)
 Dembo, Amir
 Course
 STATS21901  Stochastic Processes
 Instructor(s)
 He, Jimmy
4. Probability and random processes [2001]
 Grimmett, Geoffrey.
 3rd ed.  Oxford ; New York : Oxford University Press, 2001.
 Description
 Book — xii, 596 p. : ill. ; 25 cm.
 Summary

 Events and their probabilities random variables and their distribution discrete random variables continuous random variables generating functions and their applications Markov chains convergence of random variables random processes stationary processes renewals queues martingales diffusion processes.
 (source: Nielsen Book Data)
 1. Events and their probabilities
 2. Random variables and their distribution
 3. Discrete random variables
 4. Continuous random variables
 5. Generating functions and their applications
 6. Markov chains
 7. Convergence of random variables
 8. Random processes
 9. Stationary processes
 10. Renewals
 11. Queues
 12. Martingales
 13. Diffusion processes Appendices Bibliography List of notation Index.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
The third edition of this successful text gives a rigorous introduction to probability theory and the discussion of the most important random processes in some depth. It includes various topics which are suitable for undergraduate courses, but are not routinely taught. It is suitable to the beginner, and provides a taste and encouragement for more advanced work. There are four main aims: 1) to provide a thorough but straightforward account of basic probability, giving the reader a natural feel for the subject unburdened by oppressive technicalities, 2) to discuss important random processes in depth with many examples. 3) to cover a range of important but less routine topics, 4) to impart to the beginner the flavour of more advanced work. The books begins with basic ideas common to many undergraduate courses in mathematics, statistics and the sciences; in concludes with topics usually found at graduate level. The ordering and numbering of material in this third edition has been mostly preserved from the second. Minor alterations and additions have been added for clearer exposition. Highlights include new sections on sampling and Markov chain Monte Carlo, geometric probability, coupling and Poisson approximation, large deviations, spatial Poisson processes, renewalreward, queueing networks, stochastic calculus, Ito's formula and option pricing in the BlackScholes model for financial markets. In addition there are many (nearly 400) new exercises and problems that are entertaining and instructive; their solutions can be found in the companion volume 'One Thousand Exercises in Probability', (OUP 2001).
(source: Nielsen Book Data)
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA273 .G74 2001  Unknown On reserve at Li and Ma Science Library 2day loan 
QA273 .G74 2001  Unknown On reserve at Li and Ma Science Library 2day loan 
MATH13601, STATS21901
 Course
 MATH13601  Stochastic Processes
 Instructor(s)
 Dembo, Amir
 Course
 STATS21901  Stochastic Processes
 Instructor(s)
 He, Jimmy