Description

Book Synopsis

From the reviews: "This book is an excellent presentation of the application of martingale theory to the theory of Markov processes, especially multidimensional diffusions. [...] This monograph can be recommended to graduate students and research workers but also to all interested in Markov processes from a more theoretical point of view." Mathematische Operationsforschung und Statistik



Table of Contents
Preliminary Material: Extension Theorems, Martingales, and Compactness.- Markov Processes, Regularity of Their Sample Paths, and the Wiener Measure.- Parabolic Partial Differential Equations.- The Stochastic Calculus of Diffusion Theory.- Stochastic Differential Equations.- The Martingale Formulation.- Uniqueness.- Ito’s Uniqueness and Uniqueness to the Martingale Problem.- Some Estimates on the Transition Probability Functions.- Explosion.- Limit Theorems.- The Non-Unique Case

Multidimensional Diffusion Processes

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    A Paperback by Daniel W. Stroock, S.R.S. Varadhan

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      Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
      Publication Date: Publication Date: 23/08/2014
      ISBN13: 9783662222010, 978-3662222010
      ISBN10:

      Description

      Book Synopsis

      From the reviews: "This book is an excellent presentation of the application of martingale theory to the theory of Markov processes, especially multidimensional diffusions. [...] This monograph can be recommended to graduate students and research workers but also to all interested in Markov processes from a more theoretical point of view." Mathematische Operationsforschung und Statistik



      Table of Contents
      Preliminary Material: Extension Theorems, Martingales, and Compactness.- Markov Processes, Regularity of Their Sample Paths, and the Wiener Measure.- Parabolic Partial Differential Equations.- The Stochastic Calculus of Diffusion Theory.- Stochastic Differential Equations.- The Martingale Formulation.- Uniqueness.- Ito’s Uniqueness and Uniqueness to the Martingale Problem.- Some Estimates on the Transition Probability Functions.- Explosion.- Limit Theorems.- The Non-Unique Case

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