On Markov processes with decomposable pseudo-differential generators
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
WRAP_Kolokoltsov_KolokMarkovdecomposable.pdf - Submitted Version - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Official URL: http://dx.doi.org/10.1080/10451120410001661250
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|
|Page Range:||pp. 1-44|
|Access rights to Published version:||Restricted or Subscription Access|
1. R.F. Bass. Uniqueness in law for pure jump type Markov processes. Probab.
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