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A Concise Introduction to the Theory of Integration
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Daniel W Stroock
This edition develops the basic theory of Fourier transform. Stroock's approach is the one taken originally by Norbert Wiener and the Parseval's formula, as well as the Fourier inversion formula via Hermite functions. New exercises and solutions have been added for this edition.
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An Introduction to Markov Processes
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Daniel W Stroock
This book provides a rigorous but elementary introduction to the theory of Markov Processes on a countable state space. It should be accessible to students with a solid undergraduate background in mathematics, including students from engineering, economics, physics, and biology. Topics covered are: Doeblin's theory, general ergodic properties, and ...
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Multidimensional diffusion processes
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Daniel W Stroock
This book is an excellent presentation of the application of martingale theory to the theory of Markov processes, especially multidimensional diffusions. This approach was initiated by Stroock and Varadhan in their famous papers. (...) The proofs and techniques are presented in such a way that an adaptation in other contexts can be easily done. (. ...
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Probability theory an analytic view
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Stroock
This revised edition is suitable for a first-year graduate course on probability theory. It is intended for students with a good grasp of introductory, undergraduate probability and a reasonably sophisticated introduction to modern analysis who now want to learn what these two topics have to say about each other. By modern standards the topics ...
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Lectures on Stochastic Analysis: Diffusion Theory
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Daniel W Stroock, J W Bruce (Editor)
This book is based on a course given at Massachusetts Institute of Technology. It is intended to be a reasonably self-contained introduction to stochastic analytic techniques that can be used in the study of certain problems. The central theme is the theory of diffusions. In order to emphasize the intuitive aspects of probabilistic techniques, ...
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Partial Differential Equations for Probabilists
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Daniel W Stroock
This book deals with equations that have played a central role in the interplay between partial differential equations and probability theory. Most of this material has been treated elsewhere, but it is rarely presented in a manner that makes it easy to understand for people whose background is probability theory. Many results are given new proofs ...
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The Legacy of Norbert Wiener: A Centennial Symposium in Honor of the 100th Anniversary of Norbert Wiener's Birth, October 8-14, 1994, Massachusetts
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Norbert Wiener, Daniel W. Stroock, I. M. Singer
This book contains lectures presented at the MIT symposium on the 100th anniversary of Norbert Wiener's birth held in October 1994. The topics reflect Wiener's main interests while emphasizing current developments. In addition to lectures dealing directly with problems on which Wiener worked, such as potential theory, harmonic analysis, Wiener ...
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Markov Processes from K. Ito's Perspective (Am-155)
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Daniel W Stroock
Kiyosi Ito'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 Ito's program. The modern theory of Markov processes was initiated by A. N. Kolmogorov. ...
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Lectures on Topics in Stochastic Differential Equations: Lectures Delivered at the Indian Institute of Science, Bangalore Under the T.I.F.R.-I.I.SC. P
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Daniel W Stroock
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An Introduction to the Analysis of Paths on a Riemannian Manifold
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Daniel W. Stroock
This book aims to bridge the gap between probability and differential geometry. It gives two constructions of Brownian motion on a Riemannian manifold: an extrinsic one where the manifold is realized as an embedded submanifold of Euclidean space and an intrinsic one based on the "rolling" map. It is then shown how geometric quantities (such as ...
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Concise Introduction to the Theory of in
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Daniel W Stroock
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