15 - Markov Point Processes

Abstract

Point processes are stochastic processes that are used to model events that occur at random intervals relative to the time axis or the space axis. Point processes can be classified as temporal point processes and spatial point processes. A temporal point process is a stochastic process that captures the time points of occurrence of events that consist of the times of isolated events scattered in time, whereas spatial point process is one that captures the points in space where events occur. A Markov point process is a stochastic process that enables interactions between points in a point process. Markov point processes are used to model many applications that include earthquakes, raindrop-size distributions, image analysis, option pricing, and ecological and forestry studies. This chapter deals with point processes, marked point processes, Markov random fields, and Markov point processes.