Invariant measures for systems of Kolmogorov equations

2017/12/02 by Davide Addona, Addona, Davide, Luciana Angiuli +3
Mathematics · #35B40 #35B41 #35K45 #37L40 #47A35 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B40 #msc:35B41 #msc:35K45 #msc:37L40 #msc:47A35

paper · pdf · doi:10.48550/arxiv.1712.00627

arxiv created 2017/12/02 · arxiv updated 2017/12/05

Abstract

In this paper we provide sufficient conditions which guarantee the existence of a system of invariant measures for semigroups associated to systems of parabolic differential equations with unbounded coefficients. We prove that these measures are absolutely continuous with respect to the Lebesgue measure and study some of their main properties. Finally, we show that they characterize the asymptotic behaviour of the semigroup at infinity.

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