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Displaying similar documents to “Large deviations for rough paths of the fractional brownian motion”

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...

Fluctuations of brownian motion with drift.

Joseph G. Conlon, Peder Olsen (1999)

Publicacions Matemàtiques

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Consider 3-dimensional Brownian motion started on the unit sphere {|x| = 1} with initial density ρ. Let ρt be the first hitting density on the sphere {|x| = t + 1}, t > 0. Then the linear operators T defined by T ρ = ρ form a semigroup with an infinitesimal generator which is approximately the square root of the Laplacian. This paper studies the analogous situation for Brownian motion with a drift , where is small in a suitable scale invariant norm.

Continuous differentiability of renormalized intersection local times in R1

Jay S. Rosen (2010)

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

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We study (2, …, ; ), the -fold renormalized self-intersection local time for brownian motion in 1. Our main result says that (2, …, ; ) is continuously differentiable in the spatial variables, with probability 1.