Some Remark on Optimal Stochastic Control with Partial Information

• Published in: Stochastic analysis and applications Vol. 23; no. 6; pp. 1305 - 1320
• Main Authors: Baghéry, Fouzia, Turpin, Isabelle, Ouknine, Youssef
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Taylor & Francis Group 01.11.2005; Taylor & Francis
• Subjects: 49L25-60G07-93E11-93E20; Calculus of variations and optimal control; Exact sciences and technology; Mathematical analysis; Mathematics; Partial differential equations; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications); Stochastic control; Stochastic flow; Stochastic processes; Viscosity solutions; Zakai equation; Stochastic control(mathematics); Stochastic analysis; Value function; Fix point; Viscosity solution; Diffusion process; Hilbert space; Optimal control (mathematics)
• ISSN: 0736-2994; 1532-9356
• DOI: 10.1080/07362990500292783

We are interested in the control problem of a partially observable diffusion process, which is initialized at a fixed point of ℝ n , and we want to characterize the associated value function. To resort to the theory of viscosity solutions depends on the possibility to translate such a problem on Hilbert spaces like L 2 (ℝ n ), and so it can not be used here. Nevertheless, a result of N. Bouleau and F. Hirsch allows us to introduce a broadened problem which fulfills the condition. The fact remains to link these two control problems.