Optimal rates, Fourth Moment Theorems and non-linear functionals of Brownian local times

Reference : Optimal rates, Fourth Moment Theorems and non-linear functionals of Brownian local times


	Document type :	Dissertations and theses : Doctoral thesis
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/20306

Title :	Optimal rates, Fourth Moment Theorems and non-linear functionals of Brownian local times
Language :	English
Author, co-author :	Campese, Simon [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit]
Publication date :	14-Oct-2014
Institution :	University of Luxembourg, Luxembourg, Luxembourg
Name of the degree :	Docteur en Mathématiques
Number of pages :	xv,118
Supervisor :	Peccati, Giovanni
President of the jury :	Nourdin, Ivan
Member of the jury :	Ledoux, Michel
	Thalmaier, Anton
	Tudor, Ciprian A.
Keywords :	[en] Malliavin calculus ; Stein's method ; limit theorems ; Brownian motion ; local times ; Markov generators
Abstract :	[en] 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.
Target :	Researchers ; Professionals ; Students
Permalink :	http://hdl.handle.net/10993/20306

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