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The Lévy–Khintchine type operators with variable Lipschitz continuous coefficients generate linear or nonlinear Markov processes and semigroups
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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.12). pp. 95123. ISSN 01788051

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Official URL: http://dx.doi.org/10.1007/s0044001002938
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 pseudodifferential generator. It is shown that a conditionally positive integrodifferential operator (of the LévyKhintchine 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 WassersteinKantorovich 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:  01788051 
Official Date:  2011 
Volume:  Vol.151 
Number:  No.12 
Page Range:  pp. 95123 
Identification Number:  10.1007/s0044001002938 
Status:  Peer Reviewed 
Publication Status:  Published 
Access rights to Published version:  Restricted or Subscription Access 
References:  [1] D. Applebaum. Levy Processes and Stochastic Calculus. Cambridge studies in advanced mathematics, v. 93. Cambridge Univ. Press, 2004. 
URI:  http://wrap.warwick.ac.uk/id/eprint/39351 
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