On solutions of Kolmogorov's equations for nonhomogeneous jump Markov processes
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Publication:2019056
DOI10.1016/J.JMAA.2013.09.043zbMATH Open1328.60192arXiv1301.6998OpenAlexW2106609178MaRDI QIDQ2019056
Author name not available (Why is that?)
Publication date: 27 March 2015
Published in: (Search for Journal in Brave)
Abstract: This paper studies three ways to construct a nonhomogeneous jump Markov process: (i) via a compensator of the random measure of a multivariate point process, (ii) as a minimal solution of the backward Kolmogorov equation, and (iii) as a minimal solution of the forward Kolmogorov equation. The main conclusion of this paper is that, for a given measurable transition intensity, commonly called a Q-function, all these constructions define the same transition function. If this transition function is regular, that is, the probability of accumulation of jumps is zero, then this transition function is the unique solution of the backward and forward Kolmogorov equations. For continuous Q-functions, Kolmogorov equations were studied in Feller's seminal paper. In particular, this paper extends Feller's results for continuous Q-functions to measurable Q-functions and provides additional results.
Full work available at URL: https://arxiv.org/abs/1301.6998
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