**Title:** Stochastic Calculus and Generalized Dirichlet Processes

**Speaker:** Professor Francesco Russo

**Speaker Info:** University of Paris XIII

**Brief Description:**

**Special Note**:

**Abstract:**

We present some aspects of ``pathwise'' stochastic calculus via regularization in relation to integrator processes which are generally not semimartingales. Significant examples include Dirichlet processes, Lyons-Zheng processes and fractional Brownian motion. A Dirichlet process is the sum of a local martingale and a zero quadratic variation process A. We will emphasize the following generalized notion of Dirichlet process; a weak Dirichlet process is the sum of a local martingale M and a process A such that [A,N]=0, where N is any martingale with respect to an underlying filtration. Obviously a Dirichlet process is a weak Dirichlet process. We will illustrate with the following applications:--- Analysis of stochastic integrals related to fluid-dynamical models considered by A. Chorin, F. Flandoli and others.

--- Stochastic differential equations with distributional drift and related stochastic control theory.

The talk will partially cover joint works with M. Errami, F. Fladoli, F. Gozzi, and G. Trutnau. Most of the works to be covered can be down-loaded from http://www-math.math.univ-paris13.fr/~russo/

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