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

Details Transition from ergodic to explosive behavior in a family of stochastic differential equations Transition from ergodic to explosive behavior in a family of stochastic differential equations

2011-05-12

arxiv.org/abs/1105.2378v1

Mathematics

Probability

35 pages, 6 figures

Scientific paper

We study a family of quadratic stochastic differential equations in the plane, motivated by applications to turbulent transport of heavy particles. Using Lyapunov functions, we find a critical parameter value $\alpha_{1}=\alpha_{2}$ such that when $\alpha_{2}>\alpha_{1}$ the system is ergodic and when $\alpha_{2}<\alpha_{1}$ solutions are not defined for all times. H\"{o}rmander's hypoellipticity theorem and geometric control theory are also utilized.

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