Kolmogorov's Equations for Jump Markov Processes with Unbounded Jump\n Rates

2016/03/07 by Eugene A. Feinberg, Feinberg, Eugene A., Manasa Mandava +3 · 2 citations
Computer Science · Mathematics · Business, Management and Accounting · #Mathematical Control Systems and Analysis #Markov Chains and Monte Carlo Methods #Advanced Queuing Theory Analysis

paper · pdf · doi:10.48550/arxiv.1603.02367

Abstract

As well-known, transition probabilities of jump Markov processes satisfy\nKolmogorov's backward and forward equations. In the seminal 1940 paper, William\nFeller investigated solutions of Kolmogorov's equations for jump Markov\nprocesses. Recently the authors solved the problem studied by Feller and showed\nthat the minimal solution of Kolmogorov's backward and forward equations is the\ntransition probability of the corresponding jump Markov process if the\ntransition rate at each state is bounded. This paper presents more general\nresults. For Kolmogorov's backward equation, the sufficient condition for the\ndescribed property of the minimal solution is that the transition rate at each\nstate is locally integrable, and for Kolmogorov's forward equation the\ncorresponding sufficient condition is that the transition rate at each state is\nlocally bounded.\n

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