Kolokoltsov, V. N. (Vasiliĭ Nikitich). (2011) The Lévy–Khintchine type operators with variable Lipschitz continuous coefficients generate linear or nonlinear Markov processes and semigroups. Probability Theory and Related Fields, Vol.151 (No.1-2). pp. 95-123. ISSN 0178-8051

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Abstract

Ito's construction of Markovian solutions to stochastic equations driven by a Lévy noise is extended to nonlinear distribution dependent integrands aiming at the effective construction of linear and nonlinear Markov semigroups and the corresponding processes with a given pseudo-differential generator. It is shown that a conditionally positive integro-differential operator (of the Lévy-Khintchine type) with variable coeffcients (diffusion, drift and Lévy measure) depending Lipschitz continuously on its parameters (position and/or its distribution) generates a linear or nonlinear Markov semigroup, where the measures are metricized by the Wasserstein-Kantorovich metrics. This is a nontrivial but natural extension to general Markov processes of a long known fact for ordinary diffusions.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Markov processes
Journal or Publication Title:	Probability Theory and Related Fields
Publisher:	Springer
ISSN:	0178-8051
Date:	2011
Volume:	Vol.151
Number:	No.1-2
Page Range:	pp. 95-123
Identification Number:	10.1007/s00440-010-0293-8
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
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URI:	http://wrap.warwick.ac.uk/id/eprint/39351

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