Law of Large Numbers for Semi-Markov inhomogeneous Random Evolutions on Banach spaces
arXiv:1304.4169
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 - to an inhomogeneous semigroup. A martingale characterization of these inhomogeneous Random Evolutions is also obtained. Finally, we present applications to inhomogeneous Lévy Random Evolutions.
arXiv commentv2: typos removed. Remark 4.14 corrected. Intro slightly changed v3: typos removed. Intro slightly changed