Sticky-reflected stochastic heat equation driven by colored noise

Keywords: stochastic heat equation, colored noise, Q-Wiener process, discontinuous coefficients, Sticky-reflected Brownian motion

Abstract

UDC 519.21

We prove the existence of a sticky-reflected solution to the heat equation on the spatial interval $[0,1]$ driven by colored noise.
The process can be interpreted as an infinite-dimensional analog of the sticky-reflected Brownian motion on the real line, but now the solution obeys the usual stochastic heat equation except for points where it reaches zero.
The solution has no noise at zero and a drift pushes it to stay positive.
The proof is based on a new approach that can also be applied to other types of SPDEs with discontinuous coefficients.

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Published
22.09.2020
How to Cite
KonarovskyiV. “Sticky-Reflected Stochastic Heat Equation Driven by Colored Noise”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, no. 9, Sept. 2020, pp. 1195-31, doi:10.37863/umzh.v72i9.6282.
Section
Research articles