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Lectures on Stochastic Flows and Applications: Lectures delivered at the Indian Institute of Science, Bangalore und the T.I.F.R. - I.I.Sc. Programme in ... Lectures on Mathematics and Physics)
Lectures on Stochastic Flows and Applications Lectures delivered at the Indian Institute of Science Bangalore und the TIFR IISc Programme in Lectures on Mathematics and Physics Author:H. Kunita These are the notes of a lecture course given by the author at the T.I.F.R. Centre, Bangalore in late 1985. The contents are divided into three chapters concluding with an extensive bibliography. Chapters 1 and 2 deal with basic properties of stochastic flows and especially of Brownian flows and their relations with local characteristics and sto... more »chastic differential equations. An appendix on the generalized Ito#^ formula, Stratonovich integral and Stratonovich stochastic differential equations has been added to Chapter 2. By the way of applications of the foregoing, limit theorems for stochastic flows, along with a unifying general limit theorem, are then presented in Chapter 3 including: - Approximation theorems for stochastic differential equations and stochastic flows, due to Bismut, Ikeda-Watanabe, Malliavin, Dowell etc. - Limit theorems for driving processes, due to Papanicolaou-Stroock-Varadhan, and - Limit theorems for stochastic differential equations, due to Khasminkii, Papanicolaou-Kohler, Kesten-Papanicolaou etc.« less