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Book
xvi, 219 p. : ill. ; 23 cm.
  • 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)9789812703712 20160528
This textbook is an introduction to probability theory using measure theory. It is designed for graduate students in a variety of fields (mathematics, statistics, economics, management, finance, computer science, and engineering) who require a working knowledge of probability theory that is mathematically precise, but without excessive technicalities. The text provides complete proofs of all the essential introductory results. Nevertheless, the treatment is focused and accessible, with the measure theory and mathematical details presented in terms of intuitive probabilistic concepts, rather than as separate, imposing subjects. In this new edition, many exercises and small additional topics have been added and existing ones expanded. The text strikes an appropriate balance, rigorously developing probability theory while avoiding unnecessary detail.
(source: Nielsen Book Data)9789812703712 20160528
Science Library (Li and Ma)
MATH-136-01, STATS-219-01
Book
xiii, 234 p. : ill. ; 25 cm.
  • Preface to Second Edition Preface to First Edition PRELIMINARIES Introduction Linear Differential Equations Linear Difference Equations Exercises FINITE MARKOV CHAINS Definitions and Examples Large-Time 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 CONTINUOUS-TIME MARKOV CHAINS Poisson Process Finite State Space Birth-and-Death 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 Feynman-Kac Formula Black-Scholes Formula Simulation Exercises Suggestions for Further Reading Index.
  • (source: Nielsen Book Data)9781584886518 20160528
Emphasizing fundamental mathematical ideas rather than proofs, "Introduction to Stochastic Processes, Second Edition" provides quick access to important foundations of probability theory applicable to problems in many fields. Assuming that you have a reasonable level of computer literacy, the ability to write simple programs, and the access to software for linear algebra computations, the author approaches the problems and theorems with a focus on stochastic processes evolving with time, rather than a particular emphasis on measure theory.For those lacking in exposure to linear differential and difference equations, the author begins with a brief introduction to these concepts. He proceeds to discuss Markov chains, optimal stopping, martingales, and Brownian motion. The book concludes with a chapter on stochastic integration. The author supplies many basic, general examples and provides exercises at the end of each chapter. New to the Second Edition: expanded chapter on stochastic integration that introduces modern mathematical finance; introduction of Girsanov transformation and the Feynman-Kac formula; expanded discussion of Ito's formula and the Black-Scholes formula for pricing options; and, new topics such as Doob's maximal inequality and a discussion on self similarity in the chapter on Brownian motion.Applicable to the fields of mathematics, statistics, and engineering as well as computer science, economics, business, biological science, psychology, and engineering, this concise introduction is an excellent resource both for students and professionals.
(source: Nielsen Book Data)9781584886518 20160528
Science Library (Li and Ma)
MATH-136-01, STATS-219-01
Book
v. : ill. ; 25 cm.
  • v. 1. The binomial asset pricing model
  • v. 2. Continuous-time models.
"Stochastic Calculus for Finance" evolved from the first ten years of the Carnegie Mellon Professional Master's program in Computational Finance. The content of this book has been used successfully with students whose mathematics background consists of calculus and calculus-based probability. The text gives both precise statements of results, plausibility arguments, and even some proofs, but more importantly intuitive explanations developed and refine through classroom experience with this material are provided. The book includes a self-contained treatment of the probability theory needed for stochastic calculus, including Brownian motion and its properties. Advanced topics include foreign exchange models, forward measures, and jump-diffusion processes. This book is being published in two volumes. This second volume develops stochastic calculus, martingales, risk-neutral pricing, exotic options and term structure models, all in continuous time. Master's level students and researchers in mathematical finance and financial engineering will find this book useful.
(source: Nielsen Book Data)9780387401010 20160528
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 calculus-based 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 discrete-time setting and Volume II builds on this foundation to develop stochastic calculus, martingales, risk-neutral pricing, exotic options, and term structure models, all in continuous time. The book includes a self-contained treatment of the probability theory needed for stochastic calculus, including Brownian motion and its properties. Advanced topics include foreign exchange models, forward measures, and jump-diffusion processes. Classroom-tested 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)9780387401003 20160528
Science Library (Li and Ma)
MATH-136-01, STATS-219-01
Book
xii, 596 p. : ill. ; 25 cm.
  • 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)9780198572237 20160528
  • 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)9780198572220 20160528
The third edition of this 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 should provide 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.
(source: Nielsen Book Data)9780198572237 20160528
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, renewal-reward, queueing networks, stochastic calculus, Ito's formula and option pricing in the Black-Scholes 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)9780198572220 20160528
Science Library (Li and Ma)
MATH-136-01, STATS-219-01
Book
xvi, 557 p. ; 24 cm.
  • 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)9780123985521 20160528
The purpose, level, and style of this new edition conform to the tenets set forth in the original preface. The authors continue with their tack of developing simultaneously theory and applications, intertwined so that they refurbish and elucidate each other. The authors have made three main kinds of changes. First, they have enlarged on the topics treated in the first edition. Second, they have added many exercises and problems at the end of each chapter. Third, and most important, they have supplied, in new chapters, broad introductory discussions of several classes of stochastic processes not dealt with in the first edition, notably martingales, renewal and fluctuation phenomena associated with random sums, stationary stochastic processes, and diffusion theory.
(source: Nielsen Book Data)9780123985521 20160528
SAL3 (off-campus storage), Science Library (Li and Ma)
MATH-136-01, STATS-219-01