A Note on Generalized Malliavin Calculus
S. V. Lototsky, B. L. Rozovskii, and D. Sele\v{s}i
TL;DR
This paper extends fundamental operators of Malliavin calculus to generalized processes in higher-order chaos spaces, broadening its applicability beyond the Gaussian setting.
Contribution
It introduces extensions of the Malliavin derivative, divergence, and Ornstein-Uhlenbeck operator to non-Gaussian, higher-order chaos processes.
Findings
Operators are successfully extended to generalized chaos spaces.
The framework enables analysis of non-Gaussian stochastic processes.
Potential applications in advanced stochastic analysis and mathematical finance.
Abstract
The Malliavin derivative, divergence operator, and the Ornstein-Uhlenbeck operator are extended from the traditional Gaussian setting to generalized processes from the higher-order chaos spaces.
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Taxonomy
TopicsStatistical Mechanics and Entropy · Advanced Thermodynamics and Statistical Mechanics · Probabilistic and Robust Engineering Design