168 citations · 436 across the 32 of their papers we have counts for
14 papers · 1 filter
Global fluctuations for 1D log-gas dynamics. (2) Covariance kernel and support
Jeremie Unterberger
We consider the hydrodynamic limit in the macroscopic regime of the coupled system of stochastic differential equations, $ dλ_t^i=\frac{1}{\sqrt{N}} dW_t^i - V'(λ_t^i) dt+ \fracβ{2…
Global fluctuations for 1D log-gas dynamics
J. Unterberger
We study in this article the hydrodynamic limit in the macroscopic regime of the coupled system of stochastic differential equations, \begin{equation} dλ_t^i=\frac{1}{\sqrt{N}} dW_…
From constructive field theory to fractional stochastic calculus. (II) Constructive proof of convergence for the Lévy area of fractional Brownian motion with Hurst index
Jacques Magnen, Jérémie Unterberger
{Let be a -dimensional fractional Brownian motion with Hurst index , or more generally a Gaussian process whose paths have the same local regulari…
From constructive field theory to fractional stochastic calculus. (I) An introduction: rough path theory and perturbative heuristics
Jacques Magnen, Jérémie Unterberger
Let be a -dimensional fractional Brownian motion with Hurst index , or more generally a Gaussian process whose paths have the same local regular…
A renormalized rough path over fractional Brownian motion
Jeremie Unterberger
We construct in this article a rough path over fractional Brownian motion with arbitrary Hurst index by (i) using the Fourier normal ordering algorithm introduced in \cite{Unt-Hold…
From constructive field theory to fractional stochastic calculus. (I) The Lévy area of fractional Brownian motion with Hurst index
J. Magnen, J. Unterberger
Let be a -dimensional fractional Brownian motion with Hurst index . Defining properly iterated integrals of is a difficult task because of…
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…
Moment estimates for solutions of linear stochastic differential equations driven by analytic fractional Brownian motion
Jérémie Unterberger
As a general rule, differential equations driven by a multi-dimensional irregular path are solved by constructing a rough path over . The domain of definition ? and also est…
Hölder-continuous rough paths by Fourier normal ordering
J. Unterberger
We construct in this article an explicit geometric rough path over arbitrary -dimensional paths with finite -variation for any . The method may be coined as 'Fou…
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…
The rough path associated to the multidimensional analytic fbm with any Hurst parameter
Samy Tindel, Jérémie Unterberger
In this paper, we consider a complex-valued d-dimensional fractional Brownian motion defined on the closure of the complex upper half-plane, called analytic fractional Brownian mot…
A central limit theorem for the rescaled Lévy area of two-dimensional fractional Brownian motion with Hurst index
Jeremie Unterberger
Let be a two-dimensional fractional Brownian motion with Hurst index . Using an analytic approximation of introduced in \cite{Unt08},…
Stochastic calculus for fractional Brownian motion with Hurst exponent : A rough path method by analytic extension
Jérémie Unterberger
The -dimensional fractional Brownian motion (FBM for short) with Hurst exponent , , is a -dimensional centered,…