Cox Point Processes Driven by Ornstein–Uhlenbeck Type Processes |
| |
Authors: | R Lechnerová K Helisová V Bene? |
| |
Institution: | (1) Private College of Economic Studies, Ltd., Lindnerova 575/1, 18000 Prague 8-Libeň, Czech Republic;(2) Department of Probability and Mathematical Statistics, Faculty of Mathematics and Physics, Charles University in Prague, Sokolovská 83, 18600 Prague 8-Karlín, Czech Republic |
| |
Abstract: | The paper is devoted to the development of Cox point processes driven by nonnegative processes of Ornstein–Uhlenbeck (OU)
type. Starting with multivariate temporal processes we develop formula for the cross pair correlation function. Further filtering
problem is studied by means of two different approaches, either with discretization in time or through the point process densities
with respect to the Poisson process. The first approach is described mainly analytically while in the second case we obtain
numerical solution by means of MCMC. The Metropolis–Hastings birth–death chain for filtering can be also used when estimating
the parameters of the model. In the second part we try to develop spatial and spatio-temporal Cox point processes driven by
a stationary OU process. The generating functional of the point process is derived which enables evaluation of basic characteristics.
Finally a simulation algorithm is given and applied.
|
| |
Keywords: | Cox process Ornstein– Uhlenbeck process Filtering |
本文献已被 SpringerLink 等数据库收录! |
|