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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.1-2). pp. 95-123. doi:10.1007/s00440-010-0293-8 ISSN 0178-8051.
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Official URL: http://dx.doi.org/10.1007/s00440-010-0293-8
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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Library of Congress Subject Headings (LCSH): | Markov processes | ||||
Journal or Publication Title: | Probability Theory and Related Fields | ||||
Publisher: | Springer | ||||
ISSN: | 0178-8051 | ||||
Official Date: | 2011 | ||||
Dates: |
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Volume: | Vol.151 | ||||
Number: | No.1-2 | ||||
Page Range: | pp. 95-123 | ||||
DOI: | 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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