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In this article spatial and temporal regularity of the solution process of a stochastic partial differential equation (SPDE) of evolutionary type with nonlinear multiplicative trace class noise is analyzed.
Stochastic evolution equations
Krylov, N. V., and Rozovskiĭ, B. L · 1979
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A submartingale type inequality with applications to stochastic evolution equations
Kotelenez, P · 1982
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An estimate of Burkholder type for stochastic processes defined by the stochastic integral
Tubaro, L · 1984
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Stochastic evolution systems
Rozovskiĭ, B. L · 1990
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Stochastic equations in infinite dimensions
Da Prato, G., and Zabczyk, J · 1992
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Theory of function spaces. II
Triebel, H · 1992
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An introduction to partial differential equations
Renardy, M., and Rogers, R. C · 1993
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A W n _ 2 W^{n}\_2 -theory of the Dirichlet problem for SPDEs in general smooth domains
Krylov, N. V · 1994
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On stochastic convolution in Banach spaces and applications
Brzeźniak, Z · 1997
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Dynamics of evolutionary equations
Sell, G. R., and You, Y · 2002
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Space-time regularity for linear stochastic evolution equations driven by spatially homogeneous noise
Brzeźniak, Z., and van Neerven, J · 2003
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Sharp Gaussian regularity on the circle, and applications to the fractional stochastic heat equation
Tindel, S., Tudor, C. A., and Viens, F · 2004
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Funktionalanalysis
Werner, D · 2005
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A concise course on stochastic partial differential equations
Prévôt, C., and Röckner, M · 2007
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Stochastic integration in UMD Banach spaces
van Neerven, J. M. A. M., Veraar, M. C., and Weis, L · 2007
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Regularities for semilinear stochastic partial differential equations
Zhang, X · 2007
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Itô’s formula in UMD Banach spaces and regularity of solutions of the Zakai equation
Brzeźniak, Z., van Neerven, J. M. A. M., Veraar, M. C., and Weis, L · 2008
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Stochastic evolution equations in UMD Banach spaces
van Neerven, J. M. A. M., Veraar, M. C., and Weis, L · 2008
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Interpolation theory
Lunardi, A · 2009
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