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arXiv · 1811.12475

Existence and uniqueness of mild solution to fractional stochastic heat equation

Kostiantyn Ralchenko·Georgiy Shevchenko
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Abstract

For a class of non-autonomous parabolic stochastic partial differential equations defined on a bounded open subset $D\subset \mathbb {R}^d$ and driven by an $L^2(D)$-valued fractional Brownian motion with the Hurst index $H>1/2$, a new result on existence and uniqueness of a mild solution is established. Compared to the existing results, the uniqueness in a fully nonlinear case is shown, not assuming the coefficient in front of the noise to be affine. Additionally, the existence of moments for the solution is established.

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Kostiantyn Ralchenko, Georgiy Shevchenko. 2018-11-29. Existence and uniqueness of mild solution to fractional stochastic heat equation. https://doi.org/10.15559/18-vmsta122

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