Abstract Functional Stochastic Evolution Equations Driven by Fractional Brownian Motion. (25th February 2014)

• Record Type: Journal Article
• Authors: McKibben, Mark A.; Webster, Micah
• Other Names: Diagana T. Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-02-25
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/516853
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : 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.