Hilbert空间中梯度系统的温和解

A. Rozkosz
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引用次数: 0

摘要

考虑了被势梯度扰动的无限维Ornstein-Uhlenbeck方程的Cauchy问题。证明了该问题温和解的存在唯一性。我们还提供了由Ornstein-Uhlenbeck算子和势决定的线性倒向随机微分方程温和解的随机表示。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On mild solutions of gradient systems in Hilbert spaces
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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