Abstract functional second-order stochastic evolution equations with applications
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McKibben, Mark A.
Type of WorkText
ProgramCenter for Data, Mathematical, and Computational Sciences
Citation of Original PublicationM. McKibben, M.Webster, “Abstract functional second-order stochastic evolution equations with applications, ” Afrika Matematika, (2017), 1-26, doi: 10.1007/s13370-017-0480-1.
Fractional Brownian motion
Stochastic evolution equation
We investigate a class of abstract second-order damped functional stochastic evolution equations driven by a fractional Brownian motion in a separable Hilbert space. The global existence of mild solutions is established under various growth and compactness conditions. The case of a nonlocal initial condition is addressed. A related convergence result is discussed, and the theory is applied to stochastic wave and beam equations, as well as a spring-mass system, for illustrative purposes.