Markov-type properties

Properties of Markov Chains

Markov properties of cluster

We show that a Poisson cluster point process is a nearest-neighbour Markov point process 2] if the clusters have uniformly bounded diameter. It is typically not a nite-range Markov point process in the sense of Ripley and Kelly 12]. Furthermore, when the parent Poisson process is replaced by a Markov or nearest-neighbour Markov point process, the resulting cluster process is also nearest-neighb...

Simulated Annealing Type Markov

Ergodic properties of Markov processes

In these notes we discuss Markov processes, in particular stochastic differential equations (SDE) and develop some tools to analyze their long-time behavior. There are several ways to analyze such properties, and our point of view will be to use systematically Liapunov functions which allow a nice characterization of the ergodic properties. In this we follow, at least in spirit, the excellent b...

Ergodic Properties of Markov Processes

Markov processes describe the time-evolution of random systems that do not have any memory. Let us demonstrate what we mean by this with the following example. Consider a switch that has two states: on and off. At the beginning of the experiment, the switch is on. Every minute after that, we throw a dice. If the dice shows 6, we flip the switch, otherwise we leave it as it is. The state of the ...