Optimal Control and Filtering of the Reproduction Law of a Branching Process |
| |
Authors: | Claudia Ceci Anna Gerardi |
| |
Institution: | (1) Dip. di Scienze, Università, di Chieti, Italy;(2) Dip. Ingegneria Elettrica, Università de LAquila, Italy |
| |
Abstract: | A finite horizon control problem for the reproduction law of a branching process is studied. Some examples with complete information are tackled via the Hamilton–Jacobi–Bellman equation. A partially observable control of the cardinality of the population using the information given by the splitting process is formulated. Though there is correlation between the state and the observations and the observation process has unbounded intensity, a Girsanov-type change of probability measure can be set and the filtering equation for the unnormalized conditional distribution (the Zakai equation) can be derived. Strong uniqueness for the Zakai equation and, as a consequence, also for the Kushner–Stratonovich equation is obtained. A separated control problem is introduced, in which the dynamics are represented by the splitting process and the unnormalized conditional distribution. By the strong uniqueness for the Zakai equation, equivalence between the partially observable control problem and the separated one is proved. |
| |
Keywords: | branching processes optimal stochastic control filtering |
本文献已被 SpringerLink 等数据库收录! |
|