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

DOI10.1090/tpms/1068zbMath1433.60059arXiv1803.10711OpenAlexW2969469428WikidataQ127355211 ScholiaQ127355211MaRDI QIDQ5230214

Kostiantyn Ralchenko, Yuliya S. Mishura, Georgiy M. Shevchenko

Publication date: 21 August 2019

Published in: Theory of Probability and Mathematical Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.10711

zbMATH Keywords

Green's functionfractional Brownian motionstochastic partial differential equation

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Nonlinear parabolic equations (35K55) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60)

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Large time behaviour of semilinear stochastic partial differential equations perturbed by a mixture of Brownian and fractional Brownian motions ⋮ On a fractional Rayleigh–Stokes equation driven by fractional Brownian motion ⋮ Parameter estimation in mixed fractional stochastic heat equation ⋮ The wave equation in the three-dimensional space driven by a general stochastic measure ⋮ Ergodic properties of the solution to a fractional stochastic heat equation, with an application to diffusion parameter estimation ⋮ Estimation of the Hurst and diffusion parameters in fractional stochastic heat equation ⋮ Decompositions of stochastic convolution driven by a white-fractional Gaussian noise ⋮ Averaging principle for a stochastic cable equation ⋮ Global variational solutions to a class of fractional SPDE’s on unbounded domains ⋮ Fractional stochastic heat equation with piecewise constant coefficients ⋮ Existence and uniqueness of mild solution to fractional stochastic heat equation ⋮ Numerical simulations of nonlinear stochastic Newell-Whitehead-Segel equation and its measurable properties

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