@inbook{5fc7b2fef5a64074b67616fe61a33b26,

title = "Semilinear stochastic integral equations in L p",

abstract = "We consider a semilinear parabolic stochastic integral equation (Formula presented.) Here t ∈ [0, T], ω in a probability space Ω,x In a σ-finite measure space B with (positive) measure Λ. The kernels aμ(t) are multiples of tμ-1. The operator A: D(A) ⊂ Lp(B) → Lp(B) is such that (–A)is a nonnegative operator. The convolution integrals aβ ⁎ Gk are stochastic convolutions with respect to independent scalar Wiener processes Wk. F: [0, T] × Ω × D((-A)θ) → Lp(B) and G: [0, T]×Ω×D((-A)θ) → Lp(B, l2) are nonlinear with suitable Lipschitz conditions. We establish an Lp-theory for this equation, including existence and uniqueness of solutions, and regularity results in terms of fractional powers of (-A) and fractional derivatives in time.",

keywords = "Nonnegative operator, Regularity, Semilinear stochastic integral equations, Singular kernel, Stochastic fractional differential equation, Volterra equation",

author = "Wolfgang Desch and Londen, {Stig Olof}",

year = "2011",

doi = "10.1007/978-3-0348-0075-4_8",

language = "English",

volume = "80",

series = "Progress in Nonlinear Differential Equations and Their Application",

publisher = "Springer US",

pages = "131--166",

booktitle = "Progress in Nonlinear Differential Equations and Their Application",

address = "United States",

}