On the Cauchy problem for parabolic SPDEs in Hölder classes.

DOI10.1214/aop/1019160112zbMath1044.60050OpenAlexW2021529479MaRDI QIDQ1872503

Remigijus Mikulevičius

Publication date: 6 May 2003

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.aop/1019160112

zbMATH Keywords

Cauchy problemparabolic stochastic partial differential equations

Mathematics Subject Classification ID

Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Related Items (20)

On the Cauchy problem for backward stochastic partial differential equations in Hölder spaces ⋮ On classical solutions of linear stochastic integro-differential equations ⋮ Existence results for linear evolution equations of parabolic type ⋮ On the stochastic Magnus expansion and its application to SPDEs ⋮ Stochastic Hölder continuity of random fields governed by a system of stochastic PDEs ⋮ Schauder estimates for stochastic transport-diffusion equations with Lévy processes ⋮ Cauchy problem of stochastic kinetic equations ⋮ A Schauder estimate for stochastic PDEs ⋮ The parametrix method for parabolic SPDEs ⋮ Backward and forward filtering under the weak Hörmander condition ⋮ Model problem for integro-differential Zakai equation with discontinuous observation processes ⋮ On the Cauchy problem for stochastic parabolic equations in Hölder spaces ⋮ SPDEs with coloured noise: Analytic and stochastic approaches ⋮ Schauder-type estimates for higher-order parabolic SPDEs ⋮ On Cauchy-Dirichlet problem for parabolic quasilinear SPDEs ⋮ On the Cauchy-Dirichlet problem in the half space for parabolic sPDEs in weighted Hölder spaces ⋮ On Hölder solutions of the integro-differential Zakai equation ⋮ \(W^{2, p}\)-solutions of parabolic SPDEs in general domains ⋮ On Cauchy-Dirichlet problem in half-space for parabolic SPDEs in weighted Hölder spaces. ⋮ On the Cauchy-Dirichlet problem in a half space for backward SPDEs in weighted Hölder spaces

Cites Work

• On the Cauchy problem for certain integro-differential operators in Sobolev and Hölder spaces
• ON THE CAUCHY PROBLEM FOR LINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS
• Linear Parabolic Stochastic PDE and Wiener Chaos
• On $L_p $-Theory of Stochastic Partial Differential Equations in the Whole Space
• On the optimal filtering of diffusion processes
• Stochastic Equations in Infinite Dimensions
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