Abstract
We consider the Cauchy problem for an infinite-dimensional Ornstein-Uhlenbeck equation perturbed by gradient of a potential. We prove some results on existence and uniqueness of mild solutions of the problem. We also provide stochastic representation of mild solutions in terms of linear backward stochastic differential equations determined by the Ornstein-Uhlenbeck operator and the potential.
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Rozkosz, A. On mild solutions of gradient systems in Hilbert spaces. centr.eur.j.math. 11, 1994–2004 (2013). https://doi.org/10.2478/s11533-013-0304-y
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DOI: https://doi.org/10.2478/s11533-013-0304-y