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.

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Year of publication:	2012
Authors:	Birrell, Jeremiah ; Herzog, David P. ; Wehr, Jan
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 122.2012, 4, p. 1519-1539
Publisher:	Elsevier
Subject:	Ergodic property \| Stochastic differential equations \| Degenerate noise \| Invariant (probability) measures \| Geometric control theory \| Lyapunov functions

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

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