On limit theorems and backward stochastic differential equations via Malliavin calculus

Abstract : This thesis is organized in three distinct parts, all of which focus on the application of the Malliavin calculus to various areas of stochastic analysis such as limit theorems, fractional stochastic calculus and regularity of the solutions to stochastic differential equations. The first part is dedicated to the asymptotic study of fractional regression models via Malliavin calculus and stochastic calculus with respect to fractional Brownian motion. The second part deals with Stein's method on the Wiener space and several results on limit theorems for functionals of Gaussian fields (long memory moving averages, self-normalized sums) are presented, along with results on the deconvolution properties of the Gamma distribution. The third and last part addresses the study of the solutions to stochastic differential equations and backward stochastic differential equations and more precisely the study of the conditions for those to have a density for which upper and lower estimates can be derived.
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Solesne Bourguin. On limit theorems and backward stochastic differential equations via Malliavin calculus. Probability [math.PR]. Université Panthéon-Sorbonne - Paris I, 2011. English. ⟨tel-00668819⟩

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