Abstract
LetE be a locally convex space endowed with a centered gaussian measure ξ. We construct a continuousE-valued brownian motionW t with covariance ξ. The main goal is to solve the SDE of Langevin type dX t=\(\sqrt {2a} \)dW t−AX t wherea andA are unbounded operators of the Cameron-Martin space of (E, ξ). It appears as the unique linear measurable extension of the solution of the classical Cauchy problemv′(t)=\(\sqrt {2a} \) u′−Av(t).
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Feyel, D., de la Pradelle, A. Brownian processes in infinite dimension. Potential Anal 4, 173–183 (1995). https://doi.org/10.1007/BF01275589
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DOI: https://doi.org/10.1007/BF01275589