Abstract
We consider a class of additive functionals of ergodic semi-Markov processes and prove that their associated Markov renewal processes have a martingale decomposition representation. This leads to two main results, a functional central limit theorem for the additive functionals of semi-Markov processes and a functional almost sure limit theorem for their corresponding empirical processes, called an almost sure functional central limit theorem.
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Oprisan, A. (2017). An Invariance Principle for Additive Functionals of Semi-Markov Processes. In: Rykov, V., Singpurwalla, N., Zubkov, A. (eds) Analytical and Computational Methods in Probability Theory. ACMPT 2017. Lecture Notes in Computer Science(), vol 10684. Springer, Cham. https://doi.org/10.1007/978-3-319-71504-9_34
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DOI: https://doi.org/10.1007/978-3-319-71504-9_34
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