On the Cauchy problem for non-local Ornstein–Uhlenbeck operators. (January 2016)

• Record Type: Journal Article
• Authors: Priola, E.; Tracà, S.
• Is Part Of: Nonlinear analysis. Volume 131(2016)
• Page Start: 182
• Page End: 205
• Publication Date: 2016-01
• Subjects: 35K15 -- 60H10 -- 60J75 -- 47D07; Ornstein–Uhlenbeck non-local operators -- Lévy processes -- Core for Markov semigroups; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.09.028
• Languages: English
• ISSNs: 0362-546X

Abstract

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.