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arXiv · 1510.08602

The ergodic problem for some subelliptic operators with unbounded coefficients

Paola Mannucci·Claudio Marchi·Nicoletta Tchou
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Abstract

We study existence and uniqueness of the invariant measure for a stochastic process with degenerate diffusion, whose infinitesimal generator is a linear subelliptic operator in the whole space R N with coefficients that may be unbounded. Such a measure together with a Liouville-type theorem will play a crucial role in two applications: the ergodic problem studied through stationary problems with vanishing discount and the long time behavior of the solution to a parabolic Cauchy problem. In both cases, the constants will be characterized in terms of the invariant measure.

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Paola Mannucci, Claudio Marchi, Nicoletta Tchou. 2015-10-29. The ergodic problem for some subelliptic operators with unbounded coefficients. https://arxiv.org/abs/1510.08602

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