Časo-prostorové bodové procesy

Abstract

The thesis deals with Cox point processes driven by processes of Ornstein-Uhlenbeck (OU) type. Processes of OU type are derived from Lévy processes. A formula for cross-correlation function of multivariate Cox point processes is derived in nonstationary and stationary case. The calculations are illustrated on an example of a process derived from inverse Gaussian Lévy process. Nonlinear filtering problem for Cox point processes driven by processes of OU type is studied as well, using a stochastic simulation based on densities of point processes and Markov chain Monte Carlo (MCMC) method. This procedure is extended for Cox point processes based on infinite activity Lévy processes. The procedure is demonstrated in detail for a case of Gamma Lévy process.