9 citations · 16 across the 11 of their papers we have counts for
12 papers
Hölder regularity of a Wiener integral in abstract space
Brice Hannebicque, Erick Herbin
In this article, we propose a way to consider processes indexed by a collection of subsets of a general set . A large class of vector spaces, manifolds a…
From almost sure local regularity to almost sure Hausdorff dimension for Gaussian fields
Erick Herbin, Benjamin Arras, Geoffroy Barruel
Fine regularity of stochastic processes is usually measured in a local way by local Hölder exponents and in a global way by fractal dimensions. Following a previous work of Adler,…
A set-indexed Ornstein-Uhlenbeck process
Paul Balança, Erick Herbin
The purpose of this article is a set-indexed extension of the well-known Ornstein-Uhlenbeck process. The first part is devoted to a stationary definition of the random field and en…
Local Hölder regularity for set-indexed processes
Erick Herbin, Alexandre Richard
In this paper, we study the Hölder regularity of set-indexed stochastic processes defined in the framework of Ivanoff-Merzbach. The first key result is a Kolmogorov-like Hölder-con…
The set-indexed Lévy process: Stationarity, Markov and sample paths properties
Erick Herbin, Ely Merzbach
We present a satisfactory definition of the important class of Lévy processes indexed by a general collection of sets. We use a new definition for increment stationarity of set-ind…
2-microlocal analysis of martingales and stochastic integrals
Paul Balança, Erick Herbin
Recently, a new approach in the fine analysis of stochastic processes sample paths has been developed to predict the evolution of the local regularity under (pseudo-)differential o…