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pro vyhledávání: '"Arras , Benjamin"'
Some Notes on Quantitative Generalized CLTs with Self-Decomposable Limiting Laws by Spectral Methods
Autor:
Arras, Benjamin
In these notes, we obtain new stability estimates for centered non-degenerate selfdecomposable probability measures on $\mathbb{R}^d$ with finite second moment and for non-degenerate symmetric $\alpha$-stable probability measures on $\mathbb{R}^d$ wi
Externí odkaz:
http://arxiv.org/abs/2305.14995
Covariance Representations, $L^p$-Poincar\'e Inequalities, Stein's Kernels and High Dimensional CLTs
Autor:
Arras, Benjamin, Houdré, Christian
Publikováno v:
High Dimensional Probability IX:The Ethereal Volume, 2023
We explore connections between covariance representations, Bismut-type formulas and Stein's method. First, using the theory of closed symmetric forms, we derive covariance representations for several well-known probability measures on $\mathbb{R}^d$,
Externí odkaz:
http://arxiv.org/abs/2204.01088
Autor:
Arras, Benjamin, Houdré, Christian
Publikováno v:
Potential Anal (2022)
Boundedness properties of operators associated with non-degenerate symmetric $\alpha$-stable, $\alpha \in (1,2)$, probability measures on $\mathbb{R}^d$ are investigated on appropriate, Euclidean or otherwise, $L^p$-spaces, $p \in (1,+\infty)$. Our a
Externí odkaz:
http://arxiv.org/abs/2005.06347
Autor:
Arras, Benjamin, Houdré, Christian
Publikováno v:
Electron. J. Probab. Volume 24 (2019), paper no. 128, 63 pp
This work explores and develops elements of Stein's method of approximation, in the infinitely divisible setting, and its connections to functional analysis. It is mainly concerned with multivariate self-decomposable laws without finite first moment
Externí odkaz:
http://arxiv.org/abs/1907.10050
Autor:
Arras, Benjamin, Houdré, Christian
Publikováno v:
Electron. J. Probab. Volume 24 (2019), paper no. 29, 33 pp
We develop a multidimensional Stein methodology for non-degenerate self-decomposable random vectors in $\mathbb{R}^d$ having finite first moment. Building on previous univariate findings, we solve an integro-partial differential Stein equation by a m
Externí odkaz:
http://arxiv.org/abs/1809.02050
We consider the problem of approximating an unknown function $u\in L^2(D,\rho)$ from its evaluations at given sampling points $x^1,\dots,x^n\in D$, where $D\subset \mathbb{R}^d$ is a general domain and $\rho$ is a probability measure. The approximati
Externí odkaz:
http://arxiv.org/abs/1805.10801
Autor:
Sreeram, Anand, Adwani, Dheeraj, Arras, Benjamin, Blomdahl, Daniel, Misztal, Pawel, Bhasin, Amit
Publikováno v:
In Construction and Building Materials 17 October 2022 352
Autor:
Arras, Benjamin, Houdré, Christian
Publikováno v:
SpringerBriefs in Probability and Mathematical Statistics, 2019
We present, in a unified way, a Stein methodology for infinitely divisible laws (without Gaussian component) having finite first moment. Based on a correlation representation, we obtain a characterizing non-local Stein operator which boils down to cl
Externí odkaz:
http://arxiv.org/abs/1712.10051
Publikováno v:
Braz. J. Probab. Stat. 34(2): 394-413 (May 2020)
In this paper we propose a new, simple and explicit mechanism allowing to derive Stein operators for random variables whose characteristic function satisfies a simple ODE. We apply this to study random variables which can be represented as linear com
Externí odkaz:
http://arxiv.org/abs/1709.01161