Semimartingle Representation of a class of Semi-Markov Dynamics
Probability
2022-07-14 v1
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.
Keywords
Cite
@article{arxiv.2207.06132,
title = {Semimartingle Representation of a class of Semi-Markov Dynamics},
author = {Anindya Goswami and Subhamay Saha and Ravishankar Kapildev Yadav},
journal= {arXiv preprint arXiv:2207.06132},
year = {2022}
}
Comments
14 pages. arXiv admin note: substantial text overlap with arXiv:2201.05859