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Displaying similar documents to “Milstein’s type schemes for fractional SDEs”

Central and non-central limit theorems for weighted power variations of fractional brownian motion

Ivan Nourdin, David Nualart, Ciprian A. Tudor (2010)

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

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In this paper, we prove some central and non-central limit theorems for renormalized weighted power variations of order ≥2 of the fractional brownian motion with Hurst parameter ∈(0, 1), where is an integer. The central limit holds for 1/2<≤1−1/2, the limit being a conditionally gaussian distribution. If <1/2 we show the convergence in 2 to a limit which only depends on the fractional brownian motion, and if >1−1/2 we show the convergence in 2 to a stochastic integral...

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.

Joint continuity of the local times of fractional brownian sheets

Antoine Ayache, Dongsheng Wu, Yimin Xiao (2008)

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

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Let ={ (), ∈ℝ } be an (, )-fractional brownian sheet with index =( , …, )∈(0, 1) defined by ()=( (), …, ()) (∈ℝ ), where , …, are independent copies of a real-valued fractional brownian sheet . We prove that if <∑ ...