arXiv subjects

Ravishankar Kapildev Yadav

Publications and source records attributed to Ravishankar Kapildev Yadav.

2 recordsLinked to original sources

arXiv2022

On Merging of Stochastic Flow of Semi-Markov Dynamics

Given a semi-Markov law, using an additional parameter, we consider a family of stochastic flows corresponding to that law. Then we suitably select a particular flow, for which we obtain expressions of the meeting and merging probabilities of a pair of semi-Markov processes, solving the same equation but having two different initial conditions. A set of sufficient conditions are also obtained under which any two solutions of the flow eventually merge with probability one.

math.PR↗

arXiv2022

Semimartingle Representation of a class of Semi-Markov Dynamics

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.

math.PR↗