Equivalence of laws and null controllability for SPDEs driven by a fractional Brownian motion |
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Authors: | Bohdan Maslowski Jan van Neerven |
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Institution: | 1. Faculty of Mathematics and Physics, Charles University in Prague, Sokolovska 83, 186 75, Prague 8, Czech Republic 2. Delft Institute of Applied Mathematics, Delft University of Technology, P.O. Box 5031, 2600 GA, Delft, The Netherlands
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Abstract: | We obtain necessary and sufficient conditions for equivalence of law for linear stochastic evolution equations driven by a general Gaussian noise by identifying the suitable space of controls for the corresponding deterministic control problem. This result is applied to semilinear (reaction-diffusion) equations driven by a fractional Brownian motion. We establish the equivalence of continuous dependence of laws of solutions to semilinear equations on the initial datum in the topology of pointwise convergence of measures and null controllability for the corresponding deterministic control problem. |
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