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6 papers · 2 filters
Moderate deviations for the chemical distance in Bernoulli percolation
Olivier Garet, Régine Marchand
In this paper, we establish moderate deviations for the chemical distance in Bernoulli percolation. The chemical distance between two points is the length of the shortest open path…
Déviations modérées de la distance chimique
Olivier Garet, Régine Marchand
In this paper, we establish moderate deviations for the chemical distance in Bernoulli percolation. The chemical distance between two points is the length of the shortest open path…
A Lévy area by Fourier normal ordering for multidimensional fractional Brownian motion with small Hurst index
Jeremie Unterberger
The main tool for stochastic calculus with respect to a multidimensional process with small Hölder regularity index is rough path theory. Once has been lifted to a rough pa…
Global existence for rough differential equations under linear growth conditions
Massimiliano Gubinelli, Antoine Lejay
We prove existence of global solutions for differential equations driven by a geometric rough path under the condition that the vector fields have linear growth. We show by an expl…
Discretizing the fractional Levy area
Andreas Neuenkirch, Samy Tindel, Jérémie Unterberger
In this article, we give sharp bounds for the Euler- and trapezoidal discretization of the Levy area associated to a d-dimensional fractional Brownian motion. We show that there ar…
A rough path over multidimensional fractional Brownian motion with arbitrary Hurst index by Fourier normal ordering
Jeremie Unterberger
Fourier normal ordering \cite{Unt09bis} is a new algorithm to construct explicit rough paths over arbitrary Hölder-continuous multidimensional paths. We apply in this article the F…