Existence and uniqueness of a mild solution to the stochastic heat equation with white and fractional noises

Mishura, Yu.; Ralchenko, K.; Shevchenko, G.

doi:10.1090/tpms/1068

Existence and uniqueness of a mild solution to the stochastic heat equation with white and fractional noises

Authors: Yu. Mishura, K. Ralchenko and G. Shevchenko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 98 (2018).
Journal: Theor. Probability and Math. Statist. 98 (2019), 149-170
MSC (2010): Primary 60H15, 35R60, 35K55, 60G22
DOI: https://doi.org/10.1090/tpms/1068
Published electronically: August 19, 2019
MathSciNet review: 3824684
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Abstract: We prove the existence and uniqueness of a mild solution for a class of nonautonomous parabolic mixed stochastic partial differential equations defined on a bounded open subset $D \subset \mathbb{R}^d$ and involving standard and fractional -valued Brownian motions. We assume that the coefficients are homogeneous, Lipschitz continuous, and the coefficient at the fractional Brownian motion is an affine function.

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