Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10527276 | Stochastic Processes and their Applications | 2012 | 21 Pages |
Abstract
We study a family of quadratic, possibly degenerate, stochastic differential equations in the plane, motivated by applications to turbulent transport of heavy particles. Using Lyapunov functions, Hörmander's hypoellipticity theorem, and geometric control theory, we find a critical parameter value α1=α2 such that when α2>α1 the system is ergodic and when α2<α1 solutions are not defined for all times.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Jeremiah Birrell, David P. Herzog, Jan Wehr,