1 research outputs found
Transition from ergodic to explosive behavior in a family of stochastic differential equations
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
such that when the system is
ergodic and when solutions are not defined for all
times. H\"{o}rmander's hypoellipticity theorem and geometric control theory are
also utilized.Comment: 35 pages, 6 figure