The transition from ergodic to explosive behavior in a family of stochastic differential equations
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.
Volume (Year): 122 (2012)
Issue (Month): 4 ()
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- Mattingly, J. C. & Stuart, A. M. & Higham, D. J., 2002. "Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise," Stochastic Processes and their Applications, Elsevier, vol. 101(2), pages 185-232, October.
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