Evaluating the small deviation probabilities for subordinated Lévy processes
Werner Linde,Zhan Shi +1 more
TLDR
In this paper, the authors studied the small deviation problem for a class of symmetric Levy processes, namely, subordinated Levy processes and gave precise estimates (up to a constant multiple in the logarithmic scale) under some mild general assumption.About:
This article is published in Stochastic Processes and their Applications.The article was published on 2004-10-01 and is currently open access. It has received 33 citations till now. The article focuses on the topics: Subordinator & Fractional Brownian motion.read more
Citations
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Journal ArticleDOI
Stable non-Gaussian random processes , by G. Samorodnitsky and M. S. Taqqu. Pp. 632. £49.50. 1994. ISBN 0-412-05171-0 (Chapman and Hall).
Journal ArticleDOI
Functional quantization rate and mean regularity of processes with an application to Lévy processes
Harald Luschgy,Gilles Pagès +1 more
TL;DR: In this article, the authors investigated the connections between the mean pathwise regularity of stochastic processes and their L^r(P)-functional quantization rates as random variables taking values in some L^p([0,T],dt)-spaces (0 < p <= r).
Journal ArticleDOI
Fractional discrete processes: Compound and mixed poisson representations
Luisa Beghin,Claudio Macci +1 more
TL;DR: In this paper, two fractional versions of a family of nonnegative integer-valued processes are considered and it is shown that their probability mass functions solve fractional Kolmogorov forward equations.
Journal ArticleDOI
Functional quantization rate and mean regularity of processes with an application to L\'evy processes
Harald Luschgy,Gilles Pagès +1 more
TL;DR: In this article, the authors investigated the connections between the mean pathwise regularity of stochastic processes and their functional quantization rates as random variables taking values in some L^p([0,T],dt)-spaces (0 < p <= r).
Posted Content
Fisher Information and Logarithmic Sobolev Inequality for Matrix Valued Functions
TL;DR: In this article, the authors prove a version of Talagrand's concentration inequality for subordinated sub-Laplacians on a compact Riemannian manifold using tools from noncommutative geometry.
References
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Journal ArticleDOI
Stable non-Gaussian random processes , by G. Samorodnitsky and M. S. Taqqu. Pp. 632. £49.50. 1994. ISBN 0-412-05171-0 (Chapman and Hall).
Journal ArticleDOI
The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities
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.