Abstract Functional Stochastic Evolution Equations Driven by Fractional Brownian Motion
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McKibben, Mark A.
Type of Work14 pages
ProgramCenter for Data, Mathematical, and Computational Sciences
Citation of Original PublicationM. McKibben, M. Webster, “Abstract Functional Stochastic Evolution Equations Driven by Fractional Brownian Motion,” Abstract and Applied Analysis, Vol 2014, Article ID 516853, 14 pages, 2014. doi:10.1155/2014/516853.
We investigate a class of abstract functional stochastic evolution equations driven by a fractional Brownian motion in a real separable Hilbert space. Global existence results concerning mild solutions are formulated under various growth and compactness conditions. Continuous dependence estimates and convergence results are also established. Analysis of three stochastic partial differential equations, including a second-order stochastic evolution equation arising in the modeling of wave phenomena and a nonlinear diffusion equation, is provided to illustrate the applicability of the general theory.