عنوان

Stochastic processes /

شابک

110700800X

شابک

9781107008007

شماره

b509959

عنوان اصلي

Stochastic processes /

نام عام مواد

[Book]

نام نخستين پديدآور

Richard F. Bass

محل نشرو پخش و غیره

New York :

نام ناشر، پخش کننده و غيره

Cambridge University Press,

تاریخ نشرو بخش و غیره

2011

نام خاص و کميت اثر

xv, 390 pages :

ساير جزييات

illustrations,

ابعاد

26 cm

عنوان فروست

Cambridge series in statistical and probabilistic mathematics ;

مشخصه جلد

33

متن يادداشت

Includes bibliographical references (pages 385-386) and index

متن يادداشت

Basic notions -- Brownian motion -- Martingales -- Markov properties of Brownian motion -- The Poisson process -- Construction of Brownian motion -- Path properties of Brownian motion -- The continuity of paths -- Continuous semimartingales -- Stochastic integrals -- Itô's formula -- Some applications of Itô's formula -- The Girsanov theorem -- Local times -- Skorokhod embedding -- The general theory of processes -- Processes with jumps -- Poisson point processes -- Framework for Markov processes -- Markov properties -- Applications of the Markov properties -- Transformations of Markov processes -- Optimal stopping -- Stochastic differential equations -- Weak solutions of SDEs -- The Ray-Knight theorems -- Brownian excursions -- Financial mathematics -- Filtering -- Convergence of probability measures -- Skorokhod representation -- The space C[0, 1] -- Gaussian processes -- The space D[0, 1] -- Applications of weak convergence -- Semigroups -- Infinitesimal generators -- Dirichlet forms -- Markov processes and SDEs -- Solving partial differential equations -- One-dimensional diffusions -- Levy processes

بدون عنوان

0

متن يادداشت

"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. "--

متن يادداشت

"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"--

موضوع مستند نشده

Stochastic analysis

شماره

ويراست

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

Bass, Richard F

تاريخ عمليات

20111213122802.0

قواعد فهرست نويسي ( بخش توصيفي )

rda

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y