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Principle Seminar of the Department of Probability Theory, Moscow State University
November 8, 2017 16:45–17:45, Moscow, MSU, auditorium 12-24
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Hitting probabilities for systems of stochastic partial
differential equations: an overview
R. C. Dalang École Polytechnique Fédérale de Lausanne
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Number of views: |
This page: | 138 | Materials: | 6 |
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Abstract:
We consider a d-dimensional random field that solves a
possibly non-linear system of stochastic partial differential
equations, such as stochastic heat or wave equations. We present
results on upper and lower bounds for the probabilities that the
random field visits a deterministic subset of $\mathbb{R}^d$, in
terms, respectively, of Hausdorff measure and Newtonian capacity
of the subset. These bounds determine the critical dimension above
which points are polar, but do not, in general, determine whether
points are polar in the critical dimension. For linear spde's, we
resolve, in joint work with Carl Mueller and Yimin Xiao, the issue
of polarity of points in the critical dimension, and
also address the question of existence of multiple points
in critical dimensions
Supplementary materials:
2017_11_08_Большой_семинар.pdf (720.7 Kb)
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