An LQ problem for the heat equation on the halfline with Dirichlet boundary control and noise

Details An LQ problem for the heat equation on the halfline with Dirichlet boundary control and noise An LQ problem for the heat equation on the halfline with Dirichlet boundary control and noise

2008-01-25

arxiv.org/abs/0801.3888v2

Mathematics

Probability

16 pages. Many misprints have been corrected

Scientific paper

We study a linear quadratic problem for a system governed by the heat equation on a halfline with Dirichlet boundary control and Dirichlet boundary noise. We show that this problem can be reformulated as a stochastic evolution equation in a certain weighted L2 space. An appropriate choice of weight allows us to prove a stronger regularity for the boundary terms appearing in the infinite dimensional state equation. The direct solution of the Riccati equation related to the associated non-stochastic problem is used to find the solution of the problem in feedback form and to write the value function of the problem.

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