Malliavin Calculus and Self Normalized Sums
Solesne Bourguin (SAMM), Ciprian Tudor (LPP)
TL;DR
This paper applies Malliavin calculus to analyze self-normalized sums of independent variables, providing a chaotic expansion and establishing a Berry-Esséen bound for various distances.
Contribution
It introduces a novel approach using Malliavin calculus to derive a chaotic expansion and Berry-Esséen bounds for self-normalized sums.
Findings
Chaotic expansion for self-normalized sums
Berry-Esséen bounds with respect to multiple distances
Enhanced understanding of the probabilistic behavior of normalized sums
Abstract
We study the self-normalized sums of independent random variables from the perspective of the Malliavin calculus. We give the chaotic expansion for them and we prove a Berry-Ess\'een bound with respect to several distances.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Stochastic processes and statistical mechanics · Financial Risk and Volatility Modeling