On the exponentials of fractional Ornstein-Uhlenbeck processes.
Matsui, Muneya, Shieh, Narn-Rueih (2009)
Electronic Journal of Probability [electronic only]
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Displaying similar documents to “A note on a Feynman-Kac-type formula.”
On the exponentials of fractional Ornstein-Uhlenbeck processes.
A type of Gauss' divergence formula on Wiener spaces.
Otobe, Yoshiki (2009)
Electronic Communications in Probability [electronic only]
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Stochastic nonlinear Schrödinger equations driven by a fractional noise, well-posedness, large deviations and support.
Gautier, Eric (2007)
Electronic Journal of Probability [electronic only]
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Intermittency properties in a hyperbolic Anderson problem
Robert C. Dalang, Carl Mueller (2009)
Annales de l'I.H.P. Probabilités et statistiques
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We study the asymptotics of the even moments of solutions to a stochastic wave equation in spatial dimension 3 with linear multiplicative spatially homogeneous gaussian noise that is white in time. Our main theorem states that these moments grow more quickly than one might expect. This phenomenon is well known for parabolic stochastic partial differential equations, under the name of intermittency. Our results seem to be the first example of this phenomenon for hyperbolic equations....
Itô's formula with respect to fractional Brownian motion and its application.
Dai, W., Heyde, C.C. (1996)
Journal of Applied Mathematics and Stochastic Analysis
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A Stroock formula for a certain class of Lévy processes and applications to finance.
Eddahbi, M., Solé, J.L., Vives, J. (2005)
Journal of Applied Mathematics and Stochastic Analysis
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Stochastic calculus with respect to fractional Brownian motion
David Nualart (2006)
Annales de la faculté des sciences de Toulouse Mathématiques
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Fractional Brownian motion (fBm) is a centered self-similar Gaussian process with stationary increments, which depends on a parameter called the Hurst index. In this conference we will survey some recent advances in the stochastic calculus with respect to fBm. In the particular case , the process is an ordinary Brownian motion, but otherwise it is not a semimartingale and Itô calculus cannot be used. Different approaches have been introduced to construct stochastic integrals with...
Itô formula and local time for the fractional Brownian sheet.
Tudor, Ciprian A., Viens, Frederi G. (2003)
Electronic Journal of Probability [electronic only]
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Ergodicity of hypoelliptic SDEs driven by fractional brownian motion
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...