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International
Conference on
Stochastic Analysis and Its Applications |
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PACIFIC INSTITUTE FOR THE MATHEMATICAL SCIENCES (PIMS) INSTITUTE OF MATHEMATICAL STATISTICS DEPARTMENT OF MATHEMATICS (UW)
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Abstracts of Tutorial TalksThese talks are intended for graduate students and recent Ph.Ds. Speaker: Masatoshi Fukushima (Osaka University, Japan) Title for Talk I: One dimensional diffusions and their Dirichlet forms Abstract: Click here to see it in pdf format. Title for Talk II: Flux for diffusions (especially its computations) Abstract: Click here to see it in pdf format. Speaker: Davar Khoshnevisan (University of Utah) Title: An Introduction to Additive Lévy Processes Abstract: ``Additive Lévy processes'' are a certain family of random fields that arise naturally when we study various concrete problems about classical Lévy processes. In these two lectures I will introduce and motivate additive Lévy process, and describe some of their properties and their applications. These are a relatively self-contained pair of talks. The prerequisites for this talk are a solid familiarity with measure-theoretic probability, and a rudimentary knowledge of [at least some] Lévy processes, although they too will be defined precisely. Click here to see the slices of the talk in pdf format: Lecture 1 and Lecture 2. Speaker: Michael Röckner (Purdue University) Title: SPDE and Invariant Measures: Part I and II Abstract: The aim of the two lectures is two give a basic introduction about the role of the Kolmogorov equations in the study of SPDE (in particular, intended to be suitable for graduate students and non-experts). We shall start with ordinary SDE and then pass to the infinite dimensional case, i.e. SPDE of evolution type. We shall particularly illustrate the significance of infinitesimally invariant measures of the underlying Kolmogorov operator. Examples will include the stochastic porous media equation. The lectures will conclude with a discussion of (probabilistically) weak versus strong solutions and how one can be useful for the other. As an application we shall derive a new result on uniqueness of infinitesimally invariant measures for the Kolmogorov operator associated with the stochastic porous media equation. Click here to see the slices of the talk in pdf format. |
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This page was last modified on Wednesday, March 8, 2006. | |