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The Class of Semi-Markov Accumulation Processes

Abstract : In this paper, we introduce a new accumulation process, the Semi-Markov Accumulation Process (SMAP). This class of processes extends the framework of continuous-time Markov Additive Processes (MAPs) by allowing the underlying environmental component to be a semi-Markov process instead of a Markov process. Next, we follow an analytic approach to derive a Master Equation formula of the Renewal type that describes the evolution of SMAPs in time. We show that under exponential holding times, a matrix exponential form analogous to the matrix exponent of a MAP is attained. Finally, we consider an application of our results where closed-form solutions are rather easy to achieve.
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Alain Jean-Marie, Eleni Vatamidou. The Class of Semi-Markov Accumulation Processes. 2nd International mini-symposium on Stochastic Models: Methods and Applications (SAMMA 2017), Tuan Phung-Duc; Ioannis Dimitriou; Eleni Vatamidou, Sep 2017, Thessaloniki, Greece. pp.#190002, ⟨10.1063/1.5043829⟩. ⟨hal-01645122⟩

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