Anna Karczewska, Jerzy Zabczyk (2000)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We study regularity of stochastic convolutions solving Volterra equations on driven by a spatially homogeneous Wiener process. General results are applied to stochastic parabolic equations with fractional powers of Laplacian.
De Bouard, Anne, Debussche, Arnaud (2009)
Electronic Journal of Probability [electronic only]
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M. Hairer, N. S. Pillai (2011)
Annales de l'I.H.P. Probabilités et statistiques
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We demonstrate that stochastic differential equations (SDEs) driven by fractional brownian motion with Hurst parameter >½ have similar ergodic properties as SDEs driven by standard brownian motion. The focus in this article is on hypoelliptic systems satisfying Hörmander’s condition. We show that such systems enjoy a suitable version of the strong Feller property and we conclude that under a standard controllability condition they admit a unique stationary solution that is physical...
L. Decreusefond (2005)
Annales de l'I.H.P. Probabilités et statistiques
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Patrick Cheridito, David Nualart (2005)
Annales de l'I.H.P. Probabilités et statistiques
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J. Šnupárková (2010)
Acta Universitatis Carolinae. Mathematica et Physica
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Lluís Quer-Sardanyons, Marta Sanz-Solé (2003)
RACSAM
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We prove existence of density for the real-valued solution to a 3-dimensional stochastic wave equation (...).