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See detailContinuous Breuer-Major theorem: tightness and non-stationarity
Campese, Simon UL; Nourdin, Ivan UL; Nualart, David

in Annals of Probability (in press)

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See detailMultivariate Gaussian approxi- mations on Markov chaoses
Campese, Simon UL; Nourdin, Ivan UL; Peccati, Giovanni UL et al

in Electronic Communications in Probability (2016), 21

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See detailApproximate Normality of High-Energy Hyperspherical Eigenfunctions
Campese, Simon UL; Marinucci, Domenico; Rossi, Maurizia UL

E-print/Working paper (2015)

Detailed reference viewed: 60 (8 UL)
See detailOptimal rates, Fourth Moment Theorems and non-linear functionals of Brownian local times
Campese, Simon UL

Doctoral thesis (2014)

The present dissertation provides contributions to three distinct topics of modern stochastic analysis, namely: (a) optimal rates of convergence in multidimensional central limit theorems (CLTs) on a ... [more ▼]

The present dissertation provides contributions to three distinct topics of modern stochastic analysis, namely: (a) optimal rates of convergence in multidimensional central limit theorems (CLTs) on a Gaussian space, (b) Fourth Moment Theorems (and associated multidimensional generalisations) in the framework of the chaos of a Markov generator and (c) CLTs for non-linear functionals of Brownian local times. [less ▲]

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See detailFourth Moment Theorems for Markov diffusion generators
Azmoodeh, Ehsan UL; Campese, Simon UL; Poly, Guillaume Joseph UL

in Journal of Functional Analysis (2014), 266(4), 23412359

Inspired by the insightful article [4], we revisit the Nualart–Peccati criterion [13] (now known as the Fourth Moment Theorem) from the point of view of spectral theory of general Markov diffusion ... [more ▼]

Inspired by the insightful article [4], we revisit the Nualart–Peccati criterion [13] (now known as the Fourth Moment Theorem) from the point of view of spectral theory of general Markov diffusion generators. We are not only able to drastically simplify all of its previous proofs, but also to provide new settings of diffusive generators (Laguerre, Jacobi) where such a criterion holds. Convergence towards Gamma and Beta distributions under moment conditions is also discussed. [less ▲]

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See detailOptimal Convergence Rates and One-Term Edgeworth Expansions for Multidimensional Functionals of Gaussian Fields
Campese, Simon UL

in ALEA: Latin American Journal of Probability and Mathematical Statistics (2013)

We develop techniques for determining the exact asymptotic speed of convergence in the multidimensional normal approximation of smooth functions of Gaussian fields. As a by-product, our findings yield ... [more ▼]

We develop techniques for determining the exact asymptotic speed of convergence in the multidimensional normal approximation of smooth functions of Gaussian fields. As a by-product, our findings yield exact limits and often give rise to one-term generalized Edgeworth expansions increasing the speed of convergence. Our main mathematical tools are Malliavin calculus, Stein's method and the Fourth Moment Theorem. This work can be seen as an extension of the results of arXiv:0803.0458 to the multi-dimensional case, with the notable difference that in our framework covariances are allowed to fluctuate. We apply our findings to exploding functionals of Brownian sheets, vectors of Toeplitz quadratic functionals and the Breuer-Major Theorem. [less ▲]

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