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Volume 8, Number 3, 2018, Pages 764-804                                                                DOI:10.11948/2018.764
Invariant measures for systems of Kolmogorov equations
Davide Addona,Luciana Angiuli,Luca Lorenzi
Keywords:Systems of Kolmogorov equations, unbounded coefficients, gradient estimates, systems of invariant measures, asymptotic behaviour.
      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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