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Hamilton–Jacobi–Bellman Equations for the Optimal Control of the Duncan–Mortensen–Zakai Equation

✍ Scribed by Fausto Gozzi; Andrzej Świech

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
285 KB
Volume
172
Category
Article
ISSN
0022-1236

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✦ Synopsis

We study a class of Hamilton Jacobi Bellman (HJB) equations associated to stochastic optimal control of the Duncan Mortensen Zakai equation. The equations are investigated in weighted L 2 spaces. We introduce an appropriate notion of weak (viscosity) solution of such equations and prove that the value function is the unique solution of the HJB equation. We apply the results to stochastic optimal control problems with partial observation and correlated noise.

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