An \(L_{p }\)-theory for stochastic integral equations

DOI10.1007/s00028-010-0092-9zbMath1231.60059OpenAlexW2021299279MaRDI QIDQ657028

Wolfgang Desch, Stieg Olof Londen

Publication date: 13 January 2012

Published in: Journal of Evolution Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00028-010-0092-9

zbMATH Keywords

regularityVolterra equationsingular kernelstochastic integral equationsnonnegative operatorstochastic fractional differential equation

Mathematics Subject Classification ID

Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Abstract integral equations, integral equations in abstract spaces (45N05) Stochastic integral equations (60H20)

Related Items (7)

A Sobolev space theory for the stochastic partial differential equations with space-time non-local operators ⋮ Regularity of stochastic integral equations driven by Poisson random measures ⋮ Volterra equations in Banach spaces with completely monotone kernels ⋮ Evolutionary equations driven by fractional Brownian motion ⋮ Some approximation results for mild solutions of stochastic fractional order evolution equations driven by Gaussian noise ⋮ A Sobolev space theory for time-fractional stochastic partial differential equations driven by Lévy processes ⋮ A Sobolev space theory for stochastic partial differential equations with time-fractional derivatives

Cites Work

• Volterra equations in Banach spaces with completely monotone kernels
• A generalization of an inequality by N. V. Krylov
• Imaginary powers of elliptic second order differential operators in \(L^ p\)-spaces
• Some results on stochastic convolutions arising in Volterra equations perturbed by noise
• Quasilinear evolutionary equations and continuous interpolation spaces.
• A parabolic Littlewood-Paley inequality with applications to parabolic equations
• Evolutionary Integral Equations and Applications
• Stochastic integration of functions with values in a Banach space
• Schauder estimates for equationswith fractional derivatives
• Space-Time Regularity of Solutions of the Parabolic Stochastic Cauchy Problem
• Équations différentielles abstraites
• Analytic semigroups and optimal regularity in parabolic problems
• Stochastic Equations in Infinite Dimensions
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