Malliavin-Stein method for variance-gamma approximation on Wiener space
By Peter Eichelsbacher, Christoph Thale. 2014
56 citations recorded by the source corpus.
We combine Malliavin calculus with Stein's method to derive bounds for the Variance-Gamma approximation of functionals of isonormal Gaussian processes, in particular of random variables living inside a fixed Wiener chaos induced by such a process. The bounds are presented in terms of Malliavin operators and norms of contractions. We show that a sequence of distributions of random variables in the second Wiener chaos converges to a Variance-Gamma distribution if and only if their moments of order two to six converge to that of a Variance-Gamma distributed random variable (six moment theorem). Moreover, simplified versions for Laplace or symmetrized Gamma distributions are presented. Also multivariate extensions and a universality result for homogeneous sums are considered.
Subfields: Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/a46dd0a61ee24bff8edd7850a2ab27753239ac8a
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In Mathematical Physics
In Statistics and Probability
Citations in the corpus
- The Variance-Gamma Distribution: A Review (2023, unknown): “VG approximations for double Wiener-Itô integrals have been studied by Azmoodeh, Eichelsbacher and Thäle [7], Eichelsbacher and Thäle [28] and Gaunt [41] via Stein’s method for VG approximation, which was first developed by Gaunt [36], for which the starting point is the Stein characterisation (2”
- On Stein's method for products of normal random variables and zero bias couplings (2013, methodology): “Eichelsbacher and Thäle [13] used the Malliavin-Stein approach to obtain bounds for variance-gamma approximation of functionals of isonormal Guassian processes.”