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.
Invariant measures for systems of Kolmogorov equations / Addona, D.; Angiuli, L.; Lorenzi, L.. - In: JOURNAL OF APPLIED ANALYSIS AND COMPUTATION. - ISSN 2156-907X. - 8:3(2018), pp. 764-804. [10.11948/2018.764]
Invariant measures for systems of Kolmogorov equations
D. Addona;L. Angiuli;L. Lorenzi
2018-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
