2022/07/13 by Anindya Goswami, Goswami, Anindya, Subhamay Saha +3
Economics, Econometrics and Finance · Mathematics · #60H20 #60K15 #AMSC 60G55 #FOS: Mathematics #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2207.06132
openalex publication_date 2022/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.