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Generalized Stochastic Heat Equations

  • David Márquez-CarrerasEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 34)

Abstract

In this article, we study some properties about the solution of generalized stochastic heat equations driven by a Gaussian noise, white in time and correlated in space, and where the diffusion operator is the inverse of a Riesz potential for any positive fractional parameter. We prove the existence and uniqueness of solution and the Hölder continuity of this solution. In time, Hölder’s parameter does not depend on the fractional parameter. However, in space, Hölder’s parameter has a different behavior depending on the fractional parameter. Finally, we show that the law of the solution is absolutely continuous with respect to Lebesgue’s measure and its density is infinitely differentiable.

Keywords

Stochastic differential partial equations Fractional derivative operators Gaussian processes Malliavin calculus 

Notes

Acknowledgements

David Márquez-Carreras was partially supported by MTM2009-07203 and 2009SGR-1360.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Facultat de MatemàtiquesUniversitat de BarcelonaBarcelonaSpain

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