Limit Theorems for Additive Functionals of Continuous Time Lattice Random Walks Delayed by a Stationary Environment

For a continuous-time lattice random walk X={Xt,t≥0} delayed by a stationary random environment, we study the asymptotic behavior, as t→∞, of the normalized additive functional ct0tfXsds, t≥0. As an auxiliary result of independent interest we establish the law of large numbers for a random reward process with stationary rewards. Our results extend those obtained in [1] for non-lattice random walks. The talk is based on the joint work with Andriy Yaroshevskiy (Taras Shevchenko National University of Kyiv)

[1] Kondratiev, Y., Mishura, Y., and Shevchenko, G. Limit theorems for additive functionals of continuous time random walks. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, Volume 151, Issue 2 , 2021 , pp. 799–820.

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