Kybernetika 42 no. 5, 539-556, 2006

Nonlinear filtering in spatio–temporal doubly stochastic point processes driven by OU processes

Michaela Prokešová and Viktor Beneš


Doubly stochastic point processes driven by non-Gaussian Ornstein-Uhlenbeck type processes are studied. The problem of nonlinear filtering is investigated. For temporal point processes the characteristic form for the differential generator of the driving process is used to obtain a stochastic differential equation for the conditional distribution. The main result in the spatio-temporal case leads to the filtering equation for the conditional mean.