A new approach to the existence of invariant measures for Markovian semigroups

Beznea L, Cimpean I, Röckner M (2019)
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES 55(2): 977-1000.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
We give a new, two-step approach to prove existence of finite invariant measures for a given Markovian semigroup. First, we fix a convenient auxiliary measure and then we prove conditions equivalent to the existence of an invariant finite measure which is absolutely continuous with respect to it. As applications, we obtain a unifying generalization of different versions for Harris' ergodic theorem which provides an answer to an open question of Tweedie. Also, we show that for a nonlinear SPDE on a Gelfand triple, the strict coercivity condition is sufficient to guarantee the existence of a unique invariant probability measure for the associated semigroup, once it satisfies a Harnack type inequality with power. A corollary of the main result shows that any uniformly bounded semigroup on L-p possesses an invariant measure and we give some applications to sectorial perturbations of Dirichlet forms.
Erscheinungsjahr
Zeitschriftentitel
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES
Band
55
Ausgabe
2
Seite(n)
977-1000
ISSN
PUB-ID

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Beznea L, Cimpean I, Röckner M. A new approach to the existence of invariant measures for Markovian semigroups. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES. 2019;55(2):977-1000.
Beznea, L., Cimpean, I., & Röckner, M. (2019). A new approach to the existence of invariant measures for Markovian semigroups. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 55(2), 977-1000. doi:10.1214/18-AIHP905
Beznea, L., Cimpean, I., and Röckner, M. (2019). A new approach to the existence of invariant measures for Markovian semigroups. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES 55, 977-1000.
Beznea, L., Cimpean, I., & Röckner, M., 2019. A new approach to the existence of invariant measures for Markovian semigroups. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 55(2), p 977-1000.
L. Beznea, I. Cimpean, and M. Röckner, “A new approach to the existence of invariant measures for Markovian semigroups”, ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, vol. 55, 2019, pp. 977-1000.
Beznea, L., Cimpean, I., Röckner, M.: A new approach to the existence of invariant measures for Markovian semigroups. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES. 55, 977-1000 (2019).
Beznea, Lucian, Cimpean, Iulian, and Röckner, Michael. “A new approach to the existence of invariant measures for Markovian semigroups”. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES 55.2 (2019): 977-1000.