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arXiv · 1505.01876

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

Enrico Priola·Stefano Tracà
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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 L\'evy 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.

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Enrico Priola, Stefano Tracà. 2015-05-07. On the Cauchy problem for non-local Ornstein--Uhlenbeck operators. https://arxiv.org/abs/1505.01876

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