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Optimal regularity for semilinear stochastic partial differential equations with multiplicative noise

Raphael Kruse ; Stig Larsson (Institutionen för matematiska vetenskaper, matematik)
Electronic Journal of Probability (1083-6489). Vol. 17 (2012), p. artikel nr 65.
[Artikel, refereegranskad vetenskaplig]

This paper deals with the spatial and temporal regularity of the unique Hilbert space valued mild solution to a semilinear stochastic parabolic partial differential equation with nonlinear terms that satisfy global Lipschitz conditions and certain linear growth bounds. It is shown that the mild solution has the same optimal regularity properties as the stochastic convolution. The proof is elementary and makes use of existing results on the regularity of the solution, in particular, the Hölder continuity with a non-optimal exponent.

Nyckelord: SPDE, Hölder continuity, temporal and spatial regularity, multiplicative noise, Lipschitz nonlinearities



Denna post skapades 2012-08-20. Senast ändrad 2014-09-02.
CPL Pubid: 162197

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Sannolikhetsteori och statistik

Chalmers infrastruktur