Markov Processes from K. Ito's Perspective (AM-155)

Autor: Daniel W. Stroock

Język:

Oprawa: Miękka

Wydawca: Princeton University Press

Dostępność: Dostępna u dostawcy

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Kiyosi It's greatest contribution to probability theory may be his introduction of stochastic differ...

Informacje o książce

Autor

Daniel W. Stroock

Język

Angielski

Oprawa

Książka - Miękka

Data wydania

2003

strony

288

EAN

9780691115436

ISBN

0691115435

Enbook ID

04640724

Wydawca

Princeton University Press

Waga

440

Wymiary

152 x 235 x 20

Pełny opis

Kiyosi It's greatest contribution to probability theory may be his introduction of stochastic differential equations to explain the Kolmogorov-Feller theory of Markov processes. Starting with the geometric ideas that guided him, this book gives an account of It's program. The modern theory of Markov processes was initiated by A. N. Kolmogorov. However, Kolmogorov's approach was too analytic to reveal the probabilistic foundations on which it rests. In particular, it hides the central role played by the simplest Markov processes: those with independent, identically distributed increments. To remedy this defect, It interpreted Kolmogorov's famous forward equation as an equation that describes the integral curve of a vector field on the space of probability measures. Thus, in order to show how It's thinking leads to his theory of stochastic integral equations, Stroock begins with an account of integral curves on the space of probability measures and then arrives at stochastic integral equations when he moves to a pathspace setting. In the first half of the book, everything is done in the context of general independent increment processes and without explicit use of It's stochastic integral calculus. In the second half, the author provides a systematic development of It's theory of stochastic integration: first for Brownian motion and then for continuous martingales. The final chapter presents Stratonovich's variation on It's theme and ends with an application to the characterization of the paths on which a diffusion is supported. The book should be accessible to readers who have mastered the essentials of modern probability theory and should provide such readers with a reasonably thorough introduction to continuous-time, stochastic processes.

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