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

Nelson Vadori; Anatoliy Swishchuk

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arXiv · 1304.4169

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

Nelson Vadori·Anatoliy Swishchuk

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Abstract

Using backward propagators, we construct inhomogeneous Random Evolutions on Banach spaces driven by (uniformly ergodic) Semi-Markov processes. After studying some of their properties (measurability, continuity, integral representation), we establish a Law of Large Numbers for such inhomogeneous Random Evolutions, and more precisely their weak convergence - in the Skorohod space $D$ - to an inhomogeneous semigroup. A martingale characterization of these inhomogeneous Random Evolutions is also obtained. Finally, we present applications to inhomogeneous L\'{e}vy Random Evolutions.

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Nelson Vadori, Anatoliy Swishchuk. 2013-04-15. Law of Large Numbers for Semi-Markov inhomogeneous Random Evolutions on Banach spaces. https://arxiv.org/abs/1304.4169

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