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On Markov processes with decomposable pseudo-differential generators
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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. doi:10.1080/10451120410001661250 ISSN 1045-1129.
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Official URL: http://dx.doi.org/10.1080/10451120410001661250
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 | ||||
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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: | Stochastics and Stochastics Reports | ||||
Publisher: | Taylor & Francis | ||||
ISSN: | 1045-1129 | ||||
Official Date: | 2004 | ||||
Dates: |
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Volume: | Vol.76 | ||||
Number: | No.1 | ||||
Page Range: | pp. 1-44 | ||||
DOI: | 10.1080/10451120410001661250 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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