We derive a Feynman-Kac formula for functionals of a stochastic hybrid system evolving according to a piecewise deterministic Markov process. We first derive a stochastic Liouville equation for the moment generator of the stochastic functional, given a particular realization of the underlying discrete Markov process; the latter generates transitions between different dynamical equations for the...

In the last years, several authors studied a class of continuous-time semi-Markov processes obtained by time-changing Markov hitting times independent subordinators. Such are governed integro-differential convolution equations generalized fractional type. The aim this paper is to develop discrete-time counterpart such theory and show relationships differences with r...

Tourist movement is a complex process, but it provides very useful information for park managers and tourist operators. This paper aims to establish a sound methodology for modelling the spatial and temporal movement of tourists, with the objectives of understanding, predicting, controlling and optimising the decisions made by them as they go about choosing the attractions they want to visit.. ...

Considered are infinite horizon semi-Markov decision processes (SMDPs) with finite state and action spaces. Total expected discounted reward and long-run average expected reward optimality criteria are reviewed. Solution methodology for each criterion is given, constraints and variance sensitivity are also discussed.