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Nonlinear filtering in spatio-temporal doubly stochastic point processes driven by OU processes. (English) Zbl 1249.60097
Summary: 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 of 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.
MSC:
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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