We study the Cauchy problem involving non-local Ornstein–Uhlenbeck operators in finite and infinite dimensions. We prove classical solvability without requiring that the Lévy measure corresponding to the large jumps part has a first finite moment. Moreover, we determine a core of regular functions which is invariant for the associated transition Markov semigroup. Such a core allows to characterize the marginal laws of the Ornstein–Uhlenbeck stochastic process as unique solutions to Fokker–Planck–Kolmogorov equations for measures.

On the Cauchy problem for non-local Ornstein--Uhlenbeck operators

PRIOLA, Enrico;
2016-01-01

Abstract

We study the Cauchy problem involving non-local Ornstein–Uhlenbeck operators in finite and infinite dimensions. We prove classical solvability without requiring that the Lévy measure corresponding to the large jumps part has a first finite moment. Moreover, we determine a core of regular functions which is invariant for the associated transition Markov semigroup. Such a core allows to characterize the marginal laws of the Ornstein–Uhlenbeck stochastic process as unique solutions to Fokker–Planck–Kolmogorov equations for measures.
2016
131
182
205
http://arxiv.org/abs/1505.01876
Non local operators, Ornstein-Uhlenbeck operators, Levy processes, Core for Markov semigroups
Priola, Enrico, Stefano Traca'
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1521094
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