Zero-sum risk-sensitive stochastic games for continuous time Markov chains

Definable Zero-Sum Stochastic Games

Definable zero-sum stochastic games involve a finite number of states and action sets, reward and transition functions that are definable in an o-minimal structure. Prominent examples of such games are finite, semi-algebraic or globally subanalytic stochastic games. We prove that the Shapley operator of any definable stochastic game with separable transition and reward functions is definable in...

Continuous Time Markov Chains

Discrete-time Markov chains are useful in simulation, since updating algorithms are easier to construct in discrete steps. They can also be useful as crude models of physical, biological, and social processes. However, in the physical and biological worlds time runs continuously, and so discrete-time mathematical models are not always appropriate. This is especially true in population biology –...

Continuous-time Markov Chains

Optimal Control and Zero-Sum Games for Markov Chains of Mean-Field Type

We show existence of an optimal control and a saddlepoint for the zero-sum games associated with payoff functionals of mean-field type, under a dynamics driven by a class of Markov chains of mean-field type.

Rate-Based Stochastic Fusion Calculus and Continuous Time Markov Chains

This paper presents a stochastic fusion calculus suitable to describe systems involving general patterns of interactions. We start from fusion calculus [8] which is a symmetric generalisation of the π-calculus, and present a rate-based stochastic fusion calculus, providing a concise and compositional way to describe the behaviour of complex systems by using probability distributions. We provide...