# David Herzog : Supports of Degenerate Diffusion Processes: The Case of Polynomial Drift and Additive Noise

We discuss methods for computing supports of degenerate diffusion processes. We assume throughout that the diffusion satisfies a stochastic differential equation on R^{d} whose drift vector field X_{0} is ``polynomial'' and whose noise coefficients are constant. The case when each component of X_{0} is of odd degree is well understood. Hence we focus our efforts on X_{0} having at least one or more components of even degree. After developing methods to handle such cases, we shall apply them to specific examples, e.g. the Galerkin truncations of the Stochastic Navier-Stokes equation, to help establish ergodic properties of the resulting diffusion. One benefit to our approach is that, to prove such consequences, all we must do is compute certain
Lie brackets.

**Category**: Probability**Duration**: 01:44:52**Date**: October 20, 2011 at 4:10 PM-
**Tags:**seminar, Probability Seminar

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