The transition from ergodic to explosive behavior in a family of stochastic differential equations

Jeremiah Birrell, David P. Herzog and Jan Wehr

Stochastic Processes and their Applications, 2012, vol. 122, issue 4, 1519-1539

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.

Keywords: Ergodic property; Stochastic differential equations; Degenerate noise; Invariant (probability) measures; Geometric control theory; Lyapunov functions (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1016/j.spa.2011.12.014

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