Semimartingle Representation of a class of Semi-Markov Dynamics

Anindya Goswami; Subhamay Saha; Ravishankar Kapildev Yadav

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arXiv · 2207.06132

Semimartingle Representation of a class of Semi-Markov Dynamics

Anindya Goswami·Subhamay Saha·Ravishankar Kapildev Yadav

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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 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.

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Anindya Goswami, Subhamay Saha, Ravishankar Kapildev Yadav. 2022-07-13. Semimartingle Representation of a class of Semi-Markov Dynamics. https://arxiv.org/abs/2207.06132

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