Journal ArticleDOI
Some exact equivalents for the Brownian motion in Hölder norm
Paolo Baldi,B. Roynette +1 more
Reads0
Chats0
TLDR
In this paper, exact approximations of small probabilities for the Wiener measure on spaces of Holder paths are given, and it turns out that most of them are easier to derive than their counterparts in the uniform norm.Abstract:
Some exact equivalents of small probabilities are given for the Wiener measure on spaces of Holder paths. It turns out that most of them are easier to derive than their counterparts in the uniform norm because of a classical result of Z. Ciesielski which makes the Brownian motion on these spaces easy to handle. In particular we study the equivalents of the probability of eB in a fixed ball, ofB in a small ball and we give applications to the speed of clustering in Strassen law.read more
Citations
More filters
MonographDOI
Mathematical foundations of infinite-dimensional statistical models
Evarist Giné,Richard Nickl +1 more
TL;DR: This chapter discusses nonparametric statistical models, function spaces and approximation theory, and the minimax paradigm, which aims to provide a model for adaptive inference oflihood-based procedures.
Book ChapterDOI
Gaussian processes: Inequalities, small ball probabilities and applications
Wenbo V. Li,Qi-Man Shao +1 more
TL;DR: In this paper, the authors focus on the inequalities, small-ball probabilities, and application of Gaussian processes, and find that the small ball probability is a key step in studying the lower limits of the Gaussian process.
Journal ArticleDOI
Mouvement brownien et espaces de besov
TL;DR: In this article, a linear brownian motion is considered as a process which belongs as to the space of continuous functions defined on [01], vanishing at the origin and endowed with the topology of uniform convergence.
Journal ArticleDOI
The Laplace method for probability measures in Banach spaces
TL;DR: In this article, the Laplace method for continuous integrals in the space of continuous functions is used to estimate the probability of large deviations of the norm of Gaussian vectors and processes with values in the spaces and.
References
More filters
Book
Brownian Motion and Stochastic Calculus
TL;DR: In this paper, the authors present a characterization of continuous local martingales with respect to Brownian motion in terms of Markov properties, including the strong Markov property, and a generalized version of the Ito rule.
Journal ArticleDOI
Some asymptotic formulas for Wiener integrals
Journal ArticleDOI
On the maximum partial sums of sequences of independent random variables
TL;DR: In this article, two fundamental limit theorems are known about S*, the one clustering around the central limit theorem and the other the law of the iterated logarithm.
Journal ArticleDOI
Small Deviations in the Functional Central Limit Theorem with Applications to Functional Laws of the Iterated Logarithm
TL;DR: In this article, a small deviation theorem of a new form for the functional central limit theorem for partial sums of independent, identically distributed finite-dimensional random vectors was proved, and applied to obtain a functional form of the Chung-Jain-Pruitt law of the iterated logarithm which is also a strong speed of convergence theorem refining Strassen's invariance principle.