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Filtering and control for point process observations. (English) Zbl 0714.93048

Recent advances in stochastic calculus, Mater. Lect. Ser., College Park/MD (USA) 1987, Prog. Autom. Inf. Syst., 1-26 (1990).
[For the entire collection see Zbl 0701.00026.]
The author considers the problems of estimation and control for signal processes given as semimartingales and point process observations whose intensities are signal dependent. First, Zakai equations are derived for filtering, smoothing, and prediction problems of estimation. Then, a minimum principle is proposed for the control of partially observed Markov chains. Finally, using a variational inequality, an approximate minimum principle for control is derived.
Reviewer: E.Yaz

MSC:

93E10 Estimation and detection in stochastic control theory
93E20 Optimal stochastic control
93E14 Data smoothing in stochastic control theory
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)

Citations:

Zbl 0701.00026