On the Cauchy problem for non-local Ornstein--Uhlenbeck operators
Analysis of PDEs
2024-05-07 v1 Probability
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.
Cite
@article{arxiv.1505.01876,
title = {On the Cauchy problem for non-local Ornstein--Uhlenbeck operators},
author = {Enrico Priola and Stefano Tracà},
journal= {arXiv preprint arXiv:1505.01876},
year = {2024}
}