Markov processes

A Markov process is a type of stochastic process that satisfies the Markov property, which means that the future state of the process depends only on the current state but not on the past states. In general, Markov processes can be classified into different types, such as discrete-time Markov chains, continuous-time Markov chains, and diffusion processes, depending on the properties of the state space and the index set. These processes have various applications in fields such as queueing theory, population dynamics, finance, and physics. In this lecture we will mainly investigate in Markov processes in continuous-time by means of advanced mathematical tools, such as measure theory, functional analysis, and PDE techniques.