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Stochastic processes /
"This comprehensive guide to stochastic processes gives a complete overview of the theory and addresses the most important applications. Pitched at a level accessible to beginning graduate students and researchers from applied disciplines, it is both a course book and a rich resource for indivi...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
2011.
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| Colección: | Cambridge series on statistical and probabilistic mathematics ;
33. |
| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | "This comprehensive guide to stochastic processes gives a complete overview of the theory and addresses the most important applications. Pitched at a level accessible to beginning graduate students and researchers from applied disciplines, it is both a course book and a rich resource for individual readers. Subjects covered include Brownian motion, stochastic calculus, stochastic differential equations, Markov processes, weak convergence of processes and semigroup theory. Applications include the Black-Scholes formula for the pricing of derivatives in financial mathematics, the Kalman-Bucy filter used in the US space program and also theoretical applications to partial differential equations and analysis. Short, readable chapters aim for clarity rather than full generality. More than 350 exercises are included to help readers put their new-found knowledge to the test and to prepare them for tackling the research literature"-- "In a first course on probability one typically works with a sequence of random variables X1,X2 ... For stochastic processes, instead of indexing the random variables by the non-negative integers, we index them by t G [0, oo) and we think of Xt as being the value at time t. The random variable could be the location of a particle on the real line, the strength of a signal, the price of a stock, and many other possibilities as well. We will also work with increasing families of s -fields {J-t}, known as filtrations. The s -field J-t is supposed to represent what we know up to time t. 1.1 Processes and s -fields Let (Q., J-, P) be a probability space. A real-valued stochastic process (or simply a process) is a map X from [0, oo) x Q. to the reals. We write Xt = Xt = X(t,?). We will impose stronger measurability conditions shortly, but for now we require that the random variables Xt be measurable with respect to J- for each t 0. A collection of s -fields J-t such that J-t C J- for each t and J-s C J-t if s t is called a filtration. Define J-t+ = P\e0J-t+e. A filtration is right continuous if J-t+ = J-t for all t 0"-- |
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| Descripción Física: | 1 online resource (xv, 390 pages) : illustrations |
| Bibliografía: | Includes bibliographical references and index. |
| ISBN: | 9781139128452 1139128450 1139115626 9781139115629 9780511997044 0511997043 9781139117791 1139117793 1107386756 9781107386754 1107221870 9781107221871 1283315009 9781283315005 9786613315007 6613315001 1139123548 9781139123549 1139113437 9781139113434 |