This paper attempts to study the optimal stopping time for semi-Markov processes (SMPs) under discount optimization criteria with unbounded cost rates. In our work, we introduce an explicit construction of equivalent decision (SMDPs). The equivalence is embodied in expected discounted functions SMPs and SMDPs, that is, every can induce a policy SMDPs such value are equal, vice versa. existence ...

The distribution of extrema and overjump functionals for the semi-continuous processes (processes that intersect positive or negative level continuously) on a Markov chain were considered by many authors( for instance, see [1] [3]). In the paper [4] the distribution of extrema for almost semi-continuous processes were treated (the processes that intersect positive or negative level by exponenti...

It is shown that sequences of generalized semi-Markov processes converge in the sense of weak convergence of random functions if associated sequences of defining elements (initial distributions, transition functions and clock time distributions) converge. This continuity or stability is used to obtain information about invariant probability measures. It is shown that there exists an invariant p...

In this paper we extend the predicate logic introduced in [BRS02] in order to deal with Semi-Markov Processes. We prove that with respect to qualitative probabilistic properties, model checking is decidable for this logic applied to Semi-Markov Processes. Furthermore we apply our logic to Probabilistic Timed Automata considering classical and urgent semantics, and considering also predicates on...

Semi-Markov processes are Markovian processes in which the firing time of the transitions is modelled by probabilistic distributions over positive reals interpreted as the probability of firing a transition at a certain moment in time. In this paper we consider the trace-based semantics of semi-Markov processes, and investigate the question of how to compare two semi-Markov processes with respe...