On solutions of Kolmogorovʼs equations for nonhomogeneous jump Markov processes

Feinberg, E A and Mandava, M and Shiryaev, A N (2014) On solutions of Kolmogorovʼs equations for nonhomogeneous jump Markov processes. Journal of Mathematical Analysis and Applications, 411 (1). 261 - 270.

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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 Fellerʼs seminal paper. In particular, this paper extends Fellerʼs results for continuous Q-functions to measurable Q-functions and provides additional results.

Affiliation: Indian School of Business
ISB Creators:
ISB CreatorsORCiD
Mandava, Mhttps://orcid.org/0000-0002-3920-7805
Item Type: Article
Additional Information: The research article was published by the author with the affiliation of Stony Brook University.
Uncontrolled Keywords: Jump Markov processes, Backward Kolmogorov equation, Forward Kolmogorov equation, Minimal non-negative solution, Transition function, Compensator
Subjects: Information Systems
Operations Management
Depositing User: Veeramani R
Date Deposited: 03 Apr 2019 12:00
Last Modified: 03 Apr 2019 12:04
URI: http://eprints.exchange.isb.edu/id/eprint/744
Publisher URL: https://doi.org/10.1016/j.jmaa.2013.09.043
Publisher OA policy: http://sherpa.mimas.ac.uk/romeo/issn/0022-247X/
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