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- W2007066261 abstract "We examine the stochastic parabolic integral equation $$begin{aligned} u+A(k_1*u) = sum _{k=1}^{infty }mathop int limits ^t_0 k_2(t-s)g^k(s,omega ,x), delta beta ^k_s end{aligned}$$ driven by the family $${beta ^k_s}_{k=1}^{infty }$$ of i.i.d. fractional Brownian motions, with Hurst index $$Hin (frac{1}{2},1)$$ . The solution $$u$$ is a function of $$t,omega , x$$ ; with $$t>0, omega $$ in a probability space, and $$xin Delta $$ , a $$sigma $$ -finite measure space with positive measure $$Lambda $$ . The integrals on the right are stochastic Skorohod integrals; the kernels $$k_1(t), k_2(t)$$ are powers of $$t$$ , i.e., multiples of $$t^{alpha -1}, t^{gamma -1}$$ , with $$alpha in (0,2), gamma in (frac{1}{2},2)$$ , respectively. The operator $$A$$ is a nonnegative linear operator of $$mathrm{dom }(A)subset L_p(Delta )$$ into $$L_p(Delta )$$ , for some $$pin [2,infty ).$$ We combine transformation techniques with Malliavin calculus including results by Nualart and Balan to develop an $$L_p$$ -theory for the equation. Fractional powers of $$A$$ and of time-derivatives are used to indicate smoothness in space $$(x)$$ , and time $$(t)$$ , respectively." @default.
- W2007066261 created "2016-06-24" @default.
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- W2007066261 date "2013-07-24" @default.
- W2007066261 modified "2023-09-27" @default.
- W2007066261 title "Evolutionary equations driven by fractional Brownian motion" @default.
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- W2007066261 doi "https://doi.org/10.1007/s40072-013-0015-1" @default.
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