Displaying similar documents to “Trees and asymptotic expansions for fractional stochastic differential equations”

Weak solutions to stochastic differential equations driven by fractional Brownian motion

J. Šnupárková (2009)

Czechoslovak Mathematical Journal

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Existence of a weak solution to the n -dimensional system of stochastic differential equations driven by a fractional Brownian motion with the Hurst parameter H ∈ ( 0 , 1 ) ∖ { 1 2 } is shown for a time-dependent but state-independent diffusion and a drift that may by split into a regular part and a singular one which, however, satisfies the hypotheses of the Girsanov Theorem. In particular, a stochastic nonlinear oscillator driven by a fractional noise is considered.

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 H ∈ ( 0 , 1 ) 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 H = 1 / 2 , 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...

Differential equations driven by fractional Brownian motion.

David Nualart, Aurel Rascanu (2002)

Collectanea Mathematica

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A global existence and uniqueness result of the solution for multidimensional, time dependent, stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H > 1/2 is proved. It is shown, also, that the solution has finite moments. The result is based on a deterministic existence and uniqueness theorem whose proof uses a contraction principle and a priori estimates.

On the regularity of stochastic currents, fractional brownian motion and applications to a turbulence model

Franco Flandoli, Massimiliano Gubinelli, Francesco Russo (2009)

Annales de l'I.H.P. Probabilités et statistiques

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We study the pathwise regularity of the map ↦()= 〈( ), d 〉, where is a vector function on ℝ belonging to some Banach space , is a stochastic process and the integral is some version of a stochastic integral defined via regularization. A continuous version of this map, seen as a random element of the topological dual of will be called . We give sufficient conditions for the current to live in some Sobolev space of distributions...