We establish that, for a Markov semi-group, $L^2$ hypocoercivity, i.e. contractivity modified norm, implies quantitative deviation bounds additive functionals of the associated process and exponential integrability hitting time sets with positive measure. Moreover, in case diffusion processes under strong hypoellipticity assumption, we prove that hypocoercivity existence Lyapunov function gener...

This paper presents some fluctuation identities for a special, but none the less quite general, class of Markov Additive Processes (MAP). Before entering our discussion on the subject we shall simply begin by defining the class of processes we intend to work with and its properties. Following Asmussen and Kella (2000) we consider a process X(t), where X(t) = X(t) +X(t), and the independent proc...

investors use different approaches to select optimal portfolio. so, optimal investment choices according to return can be interpreted in different models. the traditional approach to allocate portfolio selection called a mean - variance explains. another approach is markov chain. markov chain is a random process without memory. this means that the conditional probability distribution of the nex...

The TCP window size process appears in the modeling of the famous Transmission Control Protocol used over the Internet. This continuous time Markov process takes its values in [0,∞), is ergodic and irreversible. It belongs to the Additive Increase Multiplicative Decrease class of processes. The sample paths are piecewise linear deterministic and the whole randomness of the dynamics comes from t...

We study an optimal stopping problem under non-exponential discounting, where the state process is a multi-dimensional continuous strong Markov process. The discount function taken to be log sub-additive, capturing decreasing impatience in behavioral economics. On strength of probabilistic potential theory, we establish existence equilibrium among sufficiently large collection equilibria, consi...