Normal Approximation for White Noise Functionals by Stein's Method and Hida Calculus
Louis H.Y. Chen, Yuh-Jia Lee, Hsin-Hung Shih
TL;DR
This paper develops a framework combining Stein's method and Hida calculus to achieve normal approximation for white noise functionals, extending previous work that used Malliavin calculus for Gaussian process functionals.
Contribution
It introduces a novel approach integrating Stein's method with Hida calculus for white noise functionals, expanding the tools for normal approximation in stochastic analysis.
Findings
Established a new framework for white noise functional approximation
Extended Stein's method to Hida calculus context
Provided theoretical results for normal approximation accuracy
Abstract
In this paper we establish a framework for normal approximation for white noise functionals by Stein's method and Hida calculus. Our work is inspired by that of Nourdin and Peccati (Probab. Theory Relat. Fields 145, 75-118, 2009), who combined Stein's method and Malliavin calculus for normal approximation for functionals of Gaussian processes.
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Taxonomy
TopicsStochastic processes and financial applications · Stochastic processes and statistical mechanics · Financial Risk and Volatility Modeling