Equivalence of laws and null controllability for SPDEs driven by a fractional Brownian motion

Details Equivalence of laws and null controllability for SPDEs driven by a fractional Brownian motion Equivalence of laws and null controllability for SPDEs driven by a fractional Brownian motion

2012-03-06

arxiv.org/abs/1203.1183v1

Mathematics

Probability

22 pages, submitted for publication

Scientific paper

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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