Theory of Probability and Mathematical Statistics
Existence and uniqueness of mild solution to stochastic heat equation with white and fractional noises
Yu. Mishura, K. Ralchenko, G. 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 $D \subset \R^d$ 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.
Keywords: Fractional Brownian motion, stochastic partial differential equation, Green's function
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