Zobrazeno 1 - 10
of 46
pro vyhledávání: '"Herbin, Erick"'
Autor:
Hannebicque, Brice, Herbin, Erick
In this article, we propose a way to consider processes indexed by a collection $\mathcal{A}$ of subsets of a general set $\mathcal{T}$. A large class of vector spaces, manifolds and continuous $\mathbb{R}$-trees are particular cases. Lattice-theoret
Externí odkaz:
http://arxiv.org/abs/2006.06060
Autor:
Hannebicque, Brice, Herbin, Érick
Publikováno v:
In Stochastic Processes and their Applications December 2022 154:154-196
Fine regularity of stochastic processes is usually measured in a local way by local H\"older exponents and in a global way by fractal dimensions. Following a previous work of Adler, we connect these two concepts for multiparameter Gaussian random fie
Externí odkaz:
http://arxiv.org/abs/1206.0605
Autor:
Balança, Paul, Herbin, Erick
Publikováno v:
Electron. Commun. Probab., 2012, 17, no. 39, 1-14
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 ends up with the proof of a complete characterization by its $L^2$-conti
Externí odkaz:
http://arxiv.org/abs/1203.5524
Autor:
Herbin, Erick, Richard, Alexandre
In this paper, we study the H\"older regularity of set-indexed stochastic processes defined in the framework of Ivanoff-Merzbach. The first key result is a Kolmogorov-like H\"older-continuity Theorem, whose novelty is illustrated on an example which
Externí odkaz:
http://arxiv.org/abs/1203.0750
Autor:
Herbin, Erick, Merzbach, Ely
We present a satisfactory definition of the important class of L\'evy processes indexed by a general collection of sets. We use a new definition for increment stationarity of set-indexed processes to obtain different characterizations of this class.
Externí odkaz:
http://arxiv.org/abs/1108.0873
Autor:
Balança, Paul, Herbin, Erick
Publikováno v:
Stochastic Process. Appl., 2012, 122, 2346-2382
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 operators. In this paper, we study the sample paths of continuous marti
Externí odkaz:
http://arxiv.org/abs/1107.6016
Autor:
Herbin, Erick, Merzbach, Ely
The set-indexed fractional Brownian motion (sifBm) has been defined by Herbin-Merzbach (2006) for indices that are subsets of a metric measure space. In this paper, the sifBm is proved to statisfy a strenghtened definition of increment stationarity.
Externí odkaz:
http://arxiv.org/abs/0706.3472
Autor:
Herbin, Erick, Merzbach, Ely
We prove that a set-indexed process is a set-indexed fractional Brownian motion if and only if its projections on all the increasing paths are one-parameter time changed fractional Brownian motions. As an application, we present an integral represent
Externí odkaz:
http://arxiv.org/abs/math/0607575
Autor:
Herbin, Erick, Merzbach, Ely
We define and study the multiparameter fractional Brownian motion. This process is a generalization of both the classical fractional Brownian motion and the multiparameter Brownian motion, when the condition of independence is relaxed. Relations with
Externí odkaz:
http://arxiv.org/abs/math/0605279