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

Yuliya Mishura; Kostiantyn Ralchenko; Georgiy Shevchenko

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arXiv · 1803.10711

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

Yuliya Mishura·Kostiantyn Ralchenko·Georgiy Shevchenko

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Abstract

We prove the existence and uniqueness of a mild solution for a class of non-autonomous parabolic mixed stochastic partial differential equations defined on a bounded open subset $D \subset \mathbb{R}^d$ and involving standard and fractional $L^2(D)$-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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Yuliya Mishura, Kostiantyn Ralchenko, Georgiy Shevchenko. 2018-03-28. Existence and uniqueness of mild solution to stochastic heat equation with white and fractional noises. https://arxiv.org/abs/1803.10711

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