Law of Large Numbers for Semi-Markov inhomogeneous Random Evolutions on\n Banach spaces

2013/04/15 by Nelson Vadori, Vadori, Nelson, Anatoliy Swishchuk +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1304.4169

openalex publication_date 2013/04/15 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

Using backward propagators, we construct inhomogeneous Random Evolutions on\nBanach spaces driven by (uniformly ergodic) Semi-Markov processes. After\nstudying some of their properties (measurability, continuity, integral\nrepresentation), we establish a Law of Large Numbers for such inhomogeneous\nRandom Evolutions, and more precisely their weak convergence - in the Skorohod\nspace D - to an inhomogeneous semigroup. A martingale characterization of\nthese inhomogeneous Random Evolutions is also obtained. Finally, we present\napplications to inhomogeneous L 'evy Random Evolutions.\n

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