Comparison inequalities on Wiener space
Reads0
Chats0
TLDR
In this article, the authors define a covariance-type operator on Wiener space, and prove corresponding non-Gaussian comparison inequalities for random fields and vectors, which extend the Sudakov-Fernique result on comparison of expected suprema of Gaussian fields.About:
This article is published in Stochastic Processes and their Applications.The article was published on 2014-04-01 and is currently open access. It has received 9 citations till now. The article focuses on the topics: Classical Wiener space & Ornstein–Uhlenbeck operator.read more
Citations
More filters
Journal ArticleDOI
Extremes of vector-valued Gaussian processes: exact asymptotics
TL;DR: In this paper, the exact asymptotics of P ( ∃ t ∈ [ 0, T ] ∀ i = 1, …, n X i ( t ) > u ) as u → ∞, for both locally stationary X i and X i ) with a non-constant generalized variance function were derived.
Journal ArticleDOI
Portmanteau inequalities on the Poisson space: mixed regimes and multidimensional clustering
TL;DR: A new inequality on the Poisson space is proved, allowing one to measure the distance between the laws of a general random vector, and of a target random element composed of Gaussian and Poisson random variables.
Posted Content
Extremes of vector-valued Gaussian processes: exact asymptotics
TL;DR: In this paper, the exact asymptotics of the Piterbarg inequality, Borell-TIS inequality, the Slepian lemma and the Pickands-Pitterbarg lemma were derived for mutually independent centered Gaussian processes with continuous sample paths.
Journal ArticleDOI
Fisher information and the fourth moment theorem
Ivan Nourdin,David Nualart +1 more
TL;DR: This work exhibits a sufficient condition, in terms of the negative moments of the norm of the Malliavin derivative, under which convergence in Fisher information to the standard Gaussian of sequences belonging to a given Wiener chaos is actually equivalent to convergence of only the fourth moment.
Journal ArticleDOI
On cross-correlogram IRF's estimators of two-output systems in spaces of continuous functions
TL;DR: In this paper, the authors studied single input-double output linear time-invariant systems and showed that the weak asymptotic normality of appropriately centred estimators in spaces of continuous functions is proved.
References
More filters
Book
The Malliavin Calculus and Related Topics
TL;DR: The Malliavin calculus as mentioned in this paper is an infinite-dimensional differential calculus on a Gaussian space, originally developed to provide a probabilistic proof to Hormander's "sum of squares" theorem, but it has found a wide range of applications in stochastic analysis.
Journal ArticleDOI
Spin Glass Theory and Beyond
TL;DR: In this paper, a detailed and self-contained presentation of the replica theory of infinite range spin glasses is presented, paying particular attention to new applications in the study of optimization theory and neural networks.
Book
Random Fields and Geometry
Robert J. Adler,Jonathan Taylor +1 more
TL;DR: Random Fields and Geometry as discussed by the authors is a comprehensive survey of the general theory of Gaussian random fields with a focus on geometric problems arising in the study of random fields, including continuity and boundedness, entropy and majorizing measures, Borell and Slepian inequalities.
Journal ArticleDOI
The one-sided barrier problem for Gaussian noise
TL;DR: In this paper, the authors considered the probability that a stationary Gaussian process with mean zero and covariance function r(τ) be nonnegative throughout a given interval of duration T. Several strict upper and lower bounds for P were given, along with some comparison theorems that relate P's for different covariance functions.
Related Papers (5)
Some Applications of the Malliavin Calculus to Sub-Gaussian and Non-Sub-Gaussian Random Fields
Andrew B. Vizcarra,Frederi Viens +1 more