Malliavin-Stein method for variance-gamma approximation on Wiener space

Stein Meets Malliavin in Normal Approximation

Stein’s method is a method of probability approximation which hinges on the solution of a functional equation. For normal approximation, the functional equation is a first-order differential equation. Malliavin calculus is an infinite-dimensional differential calculus whose operators act on functionals of general Gaussian processes. Nourdin and Peccati (Probab. Theory Relat. Fields 145(1–2), 75...

Variance-Gamma approximation via Stein’s method

Variance-Gamma distributions are widely used in financial modelling and contain as special cases the normal, Gamma and Laplace distributions. In this paper we extend Stein’s method to this class of distributions. In particular, we obtain a Stein equation and smoothness estimates for its solution. This Stein equation has the attractive property of reducing to the known normal and Gamma Stein equ...

Variance Reduction Methods for Simulation of Densities on Wiener Space

We develop a general error analysis framework for the Monte Carlo simulation of densities for functionals in Wiener space. We also study variance reduction methods with the help of Malliavin derivatives. For this, we give some general heuristic principles which are applied to di usion processes. A comparison with kernel density estimates is made. Departament d'Economia, Universitat Pompeu Fabra...

Stein-chen Method for Poisson Approximation

Stein Type Estimators for Disturbance Variance in Linear Regression Model

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