Dynkin同构定理与随机heat equation
Dynkin's isomorphism theorem and the stochastic heat equation
摘要：
考虑随机热方程$\partial_t u = \sL u + \dot{W}$，其中$\sL$是对偶中[Borel右]马尔可夫过程的生成元。我们表明，该解决方案是局部相互绝对连续的光滑扰动的高斯过程相关联的，通过Dynkin的同构定理，到本地时间的复制对称过程，对应于$\sL$ .在$\sL$的情况下，是一个发电机的Lévy过程$\R^d$，我们的结果给出了概率的解释，最近的研究结果Foondun等人。
英文摘要：
Consider the stochastic heat equation $\partial_t u = \sL u + \dot{W}$, where $\sL$ is the generator of a [Borel right] Markov process in duality. We show that the solution is locally mutually absolutely continuous with respect to a smooth perturbation of the Gaussian process that is associated, via Dynkin's isomorphism theorem, to the local times of the replica-symmetric process that corresponds to $\sL$.In the case that $\sL$ is the generator of a Lévy process on $\R^d$, our result gives a probabilistic explanation of the recent findings of Foondun et al.
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