On semi-Markov processes and their Kolmogorov's integro-differential\n equations

2017/01/11 by Enzo Orsingher, Orsingher, Enzo, Costantino Ricciuti +3 · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · #60G51 #60J25 #60K15 #FOS: Mathematics #Mathematical Control Systems and Analysis #Probability (math.PR) #Stochastic processes and financial applications #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1701.02905

openalex publication_date 2017/01/11 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

Semi-Markov processes are a generalization of Markov processes since the\nexponential distribution of time intervals is replaced with an arbitrary\ndistribution. This paper provides an integro-differential form of the\nKolmogorov's backward equations for a large class of homogeneous semi-Markov\nprocesses, having the form of an abstract Volterra integro-differential\nequation. An equivalent evolutionary (differential) form of the equations is\nalso provided. Fractional equations in the time variable are a particular case\nof our analysis. Weak limits of semi-Markov processes are also considered and\ntheir corresponding integro-differential Kolmogorov's equations are identified.\n

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