Semilinear Stochastic Equations in a Hilbert Space with a Fractional Brownian Motion | Zendy

T. E. Duncan | Zendy; Bohdan Maslowski | Zendy; B. PasikDuncan | Zendy

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Semilinear Stochastic Equations in a Hilbert Space with a Fractional Brownian Motion

Author(s) -

T. E. Duncan,

Bohdan Maslowski,

B. PasikDuncan

Publication year - 2009

Publication title -

siam journal on mathematical analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.882

H-Index - 92

eISSN - 1095-7154

pISSN - 0036-1410

DOI - 10.1137/08071764x

Subject(s) - mathematics , uniqueness , mathematical analysis , fractional brownian motion , stochastic partial differential equation , brownian motion , hilbert space , stochastic differential equation , nonlinear system , measure (data warehouse) , differential equation , statistics , physics , quantum mechanics , database , computer science

. 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 as- sociated linear equation. Some examples of stochastic differential and partial differential equations are given that satisfy the assumptions for the solutions of the semilinear equations. Key Words: Semilinear stochastic equations, fractional Brownian motion, stochastic partial dif-

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