From almost sure local regularity to almost sure Hausdorff dimension for gaussian fields

Erick Herbin; Benjamin Arras; Geoffroy Barruel

Displaying similar documents to “From almost sure local regularity to almost sure Hausdorff dimension for gaussian fields”

α-time fractional Brownian motion: PDE connections and local times

Erkan Nane, Dongsheng Wu, Yimin Xiao (2012)

ESAIM: Probability and Statistics

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For 0 < ≤ 2 and 0 < < 1, an -time fractional Brownian motion is an iterated process = {() = (()) ≥ 0} obtained by taking a fractional Brownian motion {() ∈ ℝ} with Hurst index 0 < < 1 and replacing the time parameter with a strictly -stable Lévy process {() ≥ 0} in ℝ independent of {() ∈ R}. It is shown that such processes have natural connections to partial differential equations and, when ...

α-time fractional brownian motion: PDE connections and local times

Erkan Nane, Dongsheng Wu, Yimin Xiao (2012)

ESAIM: Probability and Statistics

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A generalized mean-reverting equation and applications

Nicolas Marie (2014)

ESAIM: Probability and Statistics

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Consider a mean-reverting equation, generalized in the sense it is driven by a 1-dimensional centered Gaussian process with Hölder continuous paths on [0] (> 0). Taking that equation in rough paths sense only gives local existence of the solution because the non-explosion condition is not satisfied in general. Under natural assumptions, by using specific methods, we show the global existence and uniqueness of the solution, its integrability, the continuity and differentiability...

Wiener integral for the coordinate process under the σ-finite measure unifying brownian penalisations

Kouji Yano (2011)

ESAIM: Probability and Statistics

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Wiener integral for the coordinate process is defined under the -finite measure unifying Brownian penalisations, which has been introduced by [Najnudel , 345 (2007) 459–466] and [Najnudel , 19. Mathematical Society of Japan, Tokyo (2009)]. Its decomposition before and after last exit time from 0 is studied. This study prepares for the author's recent study [K. Yano, 258 (2010) 3492–3516] of Cameron-Martin formula for the -finite measure.

Lp-theory for the stochastic heat equation with infinite-dimensional fractional noise

Raluca M. Balan (2011)

ESAIM: Probability and Statistics

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In this article, we consider the stochastic heat equation $d u = (Δ u + f (t, x)) d t + \sum_{k = 1}^{\infty} g^{k} (t, x) δ β_{t}^{k}, t \in [0, T]$ , with random coefficients and , driven by a sequence () of i.i.d. fractional Brownian motions of index . Using the Malliavin calculus techniques and a -th moment maximal inequality for the infinite sum of Skorohod integrals with respect to (), we prove that the equation has a unique solution (in a Banach space of summability exponent ≥ 2), and this solution is Hölder continuous in both time and space.

Density of paths of iterated Lévy transforms of brownian motion

Marc Malric (2012)

ESAIM: Probability and Statistics

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The Lévy transform of a Brownian motion is the Brownian motion given by = sgn()d; call the Brownian motion obtained from by iterating times this transformation. We establish that almost surely, the sequence of paths ( → ) is dense in Wiener space, for the topology of uniform convergence on compact time intervals.

Density of paths of iterated Lévy transforms of Brownian motion

Marc Malric (2012)

ESAIM: Probability and Statistics

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Large deviations for directed percolation on a thin rectangle

Jean-Paul Ibrahim (2011)

ESAIM: Probability and Statistics

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Following the recent investigations of Baik and Suidan in [(2005) 325–337] and Bodineau and Martin in [10 (2005) 105–112 (electronic)], we prove large deviation properties for a last-passage percolation model in ℤ whose paths are close to the axis. The results are mainly obtained when the random weights are Gaussian or have a finite moment-generating function and rely, as in [J. Baik and T.M. Suidan, (2005) 325–337] and [T. Bodineau and J. Martin, 10 (2005) 105–112 (electronic)],...

Densité des orbites des trajectoires browniennes sous l’action de la transformation de Lévy

Jean Brossard, Christophe Leuridan (2012)

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

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Let be a measurable transformation of a probability space $(E, ℰ, π)$ , preserving the measure. Let be a random variable with law . Call (⋅, ⋅) a regular version of the conditional law of given (). Fix $B \in ℰ$ . We first prove that if is reachable from -almost every point for a Markov chain of kernel , then the -orbit of -almost every point visits . We then apply this result to the Lévy transform, which transforms the Brownian motion into the Brownian motion || − , where is the local time at 0...