Displaying similar documents to “Singularity functions for fractional processes : application to the fractional brownian sheet”

Milstein’s type schemes for fractional SDEs

Mihai Gradinaru, Ivan Nourdin (2009)

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

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Weighted power variations of fractional brownian motion are used to compute the exact rate of convergence of some approximating schemes associated to one-dimensional stochastic differential equations (SDEs) driven by . The limit of the error between the exact solution and the considered scheme is computed explicitly.

Multiparameter multifractional brownian motion : local nondeterminism and joint continuity of the local times

Antoine Ayache, Narn-Rueih Shieh, Yimin Xiao (2011)

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

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By using a wavelet method we prove that the harmonisable-type -parameter multifractional brownian motion (mfBm) is a locally nondeterministic gaussian random field. This nice property then allows us to establish joint continuity of the local times of an (, )-mfBm and to obtain some new results concerning its sample path behavior.

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.