Semimartingale Representation of a Class of Semi-Markov Dynamics

Anindya Goswami (), Subhamay Saha () and Ravishankar Kapildev Yadav ()
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Anindya Goswami: IISER Pune
Subhamay Saha: IIT Guwahati
Ravishankar Kapildev Yadav: IISER Pune

Journal of Theoretical Probability, 2024, vol. 37, issue 1, 489-510

Abstract: Abstract We consider a class of semi-Markov processes (SMP) such that the embedded discrete-time Markov chain may be non-homogeneous. The corresponding augmented processes are represented as semi-martingales using a stochastic integral equation involving a Poisson random measure. The existence and uniqueness of the equation are established. Subsequently, we show that the solution is indeed a SMP with desired transition rate. Finally, we derive the law of the bivariate process obtained from two solutions of the equation having two different initial conditions.

Keywords: Poisson random measure; Non-homogeneous semi-Markov processes; Semi-Markov system; 60G55; 60H20; 60K15 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-023-01259-4

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