SEMILINEAR STOCHASTIC EQUATIONS IN A HILBERT SPACE WITH A FRACTIONAL BROWNIAN MOTION
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...
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| Veröffentlicht in: | SIAM journal on mathematical analysis 2009-01, Vol.40 (6), p.2286-2315 |
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| creator | DUNCAN, T. E MASLOWSKI, B PASIK-DUNCAN, B |
| description | 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. |
| doi_str_mv | 10.1137/08071764X |
| format | Article |
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| source | LOCUS - SIAM's Online Journal Archive |
| subjects | Applied mathematics Brownian motion Continuity Differential equations Exact sciences and technology Functional analysis Hilbert space Integrals Linear equations Mathematical analysis Mathematical functions Mathematics Noise Numerical analysis Numerical analysis. Scientific computation Numerical methods in probability and statistics Partial differential equations, boundary value problems Partial differential equations, initial value problems and time-dependant initial-boundary value problems Sciences and techniques of general use Stochasticity Transformations Uniqueness |
| title | SEMILINEAR STOCHASTIC EQUATIONS IN A HILBERT SPACE WITH A FRACTIONAL BROWNIAN MOTION |
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