Semilinear stochastic equations in a Hilbert space with a fractional Brownian motion

View/ Open
Issue Date
2009-02-01Author
Duncan, Tyrone E.
Maslowski, Bozenna J.
Pasik-Duncan, Bozenna
Publisher
Society for Industrial and Applied Mathematics
Type
Article
Article Version
Scholarly/refereed, publisher version
Metadata
Show full item recordAbstract
The solutions of a family of semilinear stochastic equations in a Hilbert space with a fractional Brownian motion are investigated. The nonlinear term in these equations has primarily only a growth condition assumption. An arbitrary member of the family of fractional Brownian motions can be used in these equations. Existence and uniqueness for both weak and mild solutions are obtained for some of these semilinear equations. The weak solutions are obtained by a measure transformation that verifies absolute continuity with respect to the measure for the solution of the associated linear equation. Some examples of stochastic differential and partial differential equations are given that satisfy the assumptions for the solutions of the semilinear equations.
Description
This is the published version, also available here: http://dx.doi.org/10.1137/08071764X.
Collections
Citation
Duncan, Tyrone E., Maslowski, B., Pasik-Duncan, B. "SEMILINEAR STOCHASTIC EQUATIONS IN A HILBERT SPACE
WITH A FRACTIONAL BROWNIAN MOTION." SIAM J. Math. Analysis. (2009) 40, 6. 2286-2315. http://www.dx.doi.org/10.1137/08071764X.
Items in KU ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.
We want to hear from you! Please share your stories about how Open Access to this item benefits YOU.