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Semilinear stochastic equations in a Hilbert space with a fractional Brownian motion
Duncan, Tyrone E. Maslowski, Bozenna J. Pasik-Duncan, Bozenna
Duncan, Tyrone E.
Maslowski, Bozenna J.
Pasik-Duncan, Bozenna
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Abstract
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.
Date
2009-02-01
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Publisher
Society for Industrial and Applied Mathematics
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Keywords
semilinear stochastic equations, fractional Brownian motion, stochastic partial differential equations, absolute continuity of measures
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.