Abstract
We study existence and uniqueness of the invariant measure for stochastic processes with degenerate diffusion, whose infinitesimal generators are linear subelliptic operators in the whole space \({{\mathbb{R}}^N}\) with possibly unbounded coefficients. 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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Mannucci, P., Marchi, C. & Tchou, N. The ergodic problem for some subelliptic operators with unbounded coefficients. Nonlinear Differ. Equ. Appl. 23, 47 (2016). https://doi.org/10.1007/s00030-016-0401-2
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DOI: https://doi.org/10.1007/s00030-016-0401-2