Kolokoltsov, V. N. (Vasiliĭ Nikitich). (2004) On Markov processes with decomposable pseudo-differential generators. Stochastics and Stochastics Reports, Vol.76 (No.1). pp. 1-44. ISSN 1045-1129

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Abstract

The paper is devoted to the study of Markov processes in finite-dimensional convex cones (especially R d and ) with a decomposable generator, i.e. with a generator of the form where every A n acts as a multiplication operator by a positive, not necessarily bounded, continuous function a n (x) and where every ψ n generates a Lévy process, i.e. a process with i.i.d. increments in R d . The following problems are discussed: (i) existence and uniqueness of Markov or Feller processes with a given generator, (ii) continuous dependence of the process on the coefficients a n and the starting points, (iii) well posedness of the corresponding martingale problem, (iv) generalized solutions to the Dirichlet problem, (v) regularity of boundary points.

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:	Stochastics and Stochastics Reports
Publisher:	Taylor & Francis
ISSN:	1045-1129
Date:	2004
Volume:	Vol.76
Number:	No.1
Page Range:	pp. 1-44
Identification Number:	10.1080/10451120410001661250
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/39211

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