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Null Controllability for Forward and Backward Stochastic Parabolic Equations
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Update time: 2009-07-22
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Null Controllability for Forward and Backward Stochastic Parabolic Equations

SIAM J. Control Optim. Volume 48, Issue 4, pp. 2191-2216 (2009)

Published June 25, 2009

 

This paper is concerned with the null controllability for general forward and backward linear stochastic parabolic equations. To develop the duality argument, we establish observability estimates for linear backward and forward stochastic parabolic equations with general coefficients, by means of a global Carleman estimate. Our Carleman inequality (Theorem 6.1) and observability estimate (Theorem 2.3) for backward stochastic parabolic equations are new in their forms. By adding a control variable to act on the white noise, we give a partial solution to the null controllability of forward stochastic heat equations, which was regarded as a challenging topic (see pages 99 and 108–110 in [Barbu, Răscanu, and Tessitore, Appl. Math. Optim., 47 (2003), pp. 97–120]).

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