Existence and uniqueness of mild solution to fractional stochastic heat equation

• Published in: Modern Stochastics: Theory and Applications Vol. 6; no. 1; pp. 57 - 79
• Main Authors: Kostiantyn Ralchenko, Georgiy Shevchenko
• Format: Journal Article
• Language: English
• Published: VTeX 01-03-2019
• Subjects: fractional Brownian motion; Green’s function; mild solution; Stochastic partial differential equation
• ISSN: 2351-6046; 2351-6054
• DOI: 10.15559/18-VMSTA122

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.