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  • Search: person:"Nourdin, Ivan"
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Year of publication
Subject
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Malliavin calculus 3 Convergence in total variation 2 Gaussian processes 2 Absolute continuity 1 Berry-Esseen bounds 1 Breuer-Major central limit theorems 1 Chaos theory 1 Chaostheorie 1 Convergence in distribution 1 Convergence in law 1 Interpolation 1 Invariance principle 1 Multiple Wiener–Itô integral 1 Ornstein–Uhlenbeck semigroup 1 Stein’s method 1 Wiener chaos 1
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Online availability
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Undetermined 7 Free 1
Type of publication
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Article 8 Book / Working Paper 2
Type of publication (narrower categories)
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Article in journal 1 Aufsatz in Zeitschrift 1
Language
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Undetermined 7 English 3
Author
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Nourdin, Ivan 10 Peccati, Giovanni 4 Podolskij, Mark 2 Poly, Guillaume 2 Bercu, Bernard 1 Noreddine, Salim 1 Simon, Thomas 1 Taqqu, Murad S. 1 Viens, Frederi G. 1
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Institution
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School of Economics and Management, University of Aarhus 1
Published in...
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Stochastic Processes and their Applications 5 Bocconi and Springer series 1 CREATES Research Papers 1 Journal of Multivariate Analysis 1 Probability theory and related fields : continuation of Zeitschrift für Wahrscheinlichkeitstheorie 1 Statistics & Probability Letters 1
Source
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RePEc 8 ECONIS (ZBW) 1 USB Cologne (EcoSocSci) 1
Showing 1 - 10 of 10
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Quantitative Breuer-Major Theorems
Nourdin, Ivan; Peccati, Giovanni; Podolskij, Mark - School of Economics and Management, University of Aarhus - 2010
We consider sequences of random variables of the type $S_n= n^{-1/2} \sum_{k=1}^n f(X_k)$, $n\geq 1$, where $X=(X_k)_{k\in \Z}$ is a $d$-dimensional Gaussian process and $f: \R^d \rightarrow \R$ is a measurable function. It is known that, under certain conditions on $f$ and the covariance...
Persistent link: https://www.econbiz.de/10008552197
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An invariance principle under the total variation distance
Nourdin, Ivan; Poly, Guillaume - In: Stochastic Processes and their Applications 125 (2015) 6, pp. 2190-2205
Let X1,X2,… be a sequence of i.i.d. random variables, with mean zero and variance one and let Sn=(X1+⋯+Xn)/n. An old and celebrated result of Prohorov (1952) asserts that Sn converges in total variation to the standard Gaussian distribution if and only if Sn0 has an absolutely continuous...
Persistent link: https://www.econbiz.de/10011209766
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Comparison inequalities on Wiener space
Nourdin, Ivan; Peccati, Giovanni; Viens, Frederi G. - In: Stochastic Processes and their Applications 124 (2014) 4, pp. 1566-1581
We define a covariance-type operator on Wiener space: for F and G two random variables in the Gross–Sobolev space D1,2 of random variables with a square-integrable Malliavin derivative, we let ΓF,G≔〈DF,−DL−1G〉, where D is the Malliavin derivative operator and L−1 is the...
Persistent link: https://www.econbiz.de/10011065100
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Convergence in total variation on Wiener chaos
Nourdin, Ivan; Poly, Guillaume - In: Stochastic Processes and their Applications 123 (2013) 2, pp. 651-674
Let {Fn} be a sequence of random variables belonging to a finite sum of Wiener chaoses. Assume further that it converges in distribution towards F∞ satisfying V ar(F∞)0. Our first result is a sequential version of a theorem by Shigekawa (1980) [23]. More precisely, we prove, without...
Persistent link: https://www.econbiz.de/10011065031
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Selected aspects of fractional Brownian motion
Nourdin, Ivan - 2012
Persistent link: https://www.econbiz.de/10009662544
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Quantitative Breuer-Major theorems
Nourdin, Ivan; Peccati, Giovanni; Podolskij, Mark - In: Stochastic Processes and their Applications 121 (2011) 4, pp. 793-812
We consider sequences of random variables of the type , n=1, where is a d-dimensional Gaussian process and is a measurable function. It is known that, under certain conditions on f and the covariance function r of X, Sn converges in distribution to a normal variable S. In the present paper we...
Persistent link: https://www.econbiz.de/10008873723
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On the Gaussian approximation of vector-valued multiple integrals
Noreddine, Salim; Nourdin, Ivan - In: Journal of Multivariate Analysis 102 (2011) 6, pp. 1008-1017
By combining the findings of two recent, seminal papers by Nualart, Peccati and Tudor, we get that the convergence in law of any sequence of vector-valued multiple integrals Fn towards a centered Gaussian random vector N, with given covariance matrix C, is reduced to just the convergence of: (i)...
Persistent link: https://www.econbiz.de/10009023468
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Almost sure central limit theorems on the Wiener space
Bercu, Bernard; Nourdin, Ivan; Taqqu, Murad S. - In: Stochastic Processes and their Applications 120 (2010) 9, pp. 1607-1628
In this paper, we study almost sure central limit theorems for sequences of functionals of general Gaussian fields. We apply our result to non-linear functions of stationary Gaussian sequences. We obtain almost sure central limit theorems for these non-linear functions when they converge in law...
Persistent link: https://www.econbiz.de/10008874200
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Stein's method on Wiener chaos
Nourdin, Ivan; Peccati, Giovanni - In: Probability theory and related fields : continuation of … 145 (2009) 1/2, pp. 75-118
Persistent link: https://www.econbiz.de/10003936341
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On the absolute continuity of one-dimensional SDEs driven by a fractional Brownian motion
Nourdin, Ivan; Simon, Thomas - In: Statistics & Probability Letters 76 (2006) 9, pp. 907-912
The problem of absolute continuity for a class of SDEs driven by a real fractional Brownian motion of any Hurst index is addressed. First, we give an elementary proof of the fact that when the diffusion coefficient does not vanish, the solution to the SDE has a positive density for all t0....
Persistent link: https://www.econbiz.de/10005319231
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