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articleFree Access
A Feynman–Kac approach for the spatial derivative of the solution to the Wick stochastic heat equation driven by time homogeneous white noise
- Hyun-Jung Kim and
- Ramiro Scorolli
Infinite Dimensional Analysis, Quantum Probability and Related Topics21 Jun 2023
Preview Abstract
We consider the (unique) mild solution $u (t, x)$ $u (t, x)$ of a one-dimensional stochastic heat equation on $[0, T] \times ℝ$ driven by time-homogeneous white noise in the Wick–Skorokhod sense. The main result of this paper is the computation of the spatial derivative of $u (t, x)$ , denoted by $\partial_{x} u (t, x)$ , and its representation as a Feynman–Kac type closed form. The chaos expansion of $\partial_{x} u (t, x)$ makes it possible to find its (optimal) Hölder regularity especially in space.

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