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Foundations of modern probability

Author: Olav Kallenberg
Publisher: New York : Springer, ©1997.
Series: Probability and its applications.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

A study of the foundations of modern probability, covering topics such as stochastic integrals and quadratic variation, martingales and optional times, Feller processes and semigroups, and Poisson  Read more...

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Document Type: Book
All Authors / Contributors: Olav Kallenberg
ISBN: 0387949577 9780387949574
OCLC Number: 318174134
Description: xii, 523 p. ; 25 cm.
Contents: Elements of measure theory; processes, distributions, and independence; random sequences, series, and sums; characteristic functions and classical limit theorems; conditioning and disintegration; Martingales and optional times; Markov property and discrete time chains; random walk and renewal theory; stationarity and ergodic theory; Poisson and pure jump type Markov processes; Gaussian processes and Brownian motion; Skorohod embedding and invariance principles; independent increment processes and null-arrays; convergence of random processes, measures, and sets; stochastic integrals and quadratic variation; continuous martingales and Brownian motion; Feller processes and semigroups; SDEs and martingale problems; local time, excursions, and additive functionals; one-dimensional SDEs and diffusions; connections with PDEs and potential theory; predictability, compensation, and excessive functions; semimartingales and stochastic integration.
Series Title: Probability and its applications.
Responsibility: Olav Kallenberg.

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