Variance-Gamma approximation via Stein's method
نویسندگان
چکیده
منابع مشابه
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...
متن کاملApproximation for the gamma function via the tri-gamma function
In this paper, we present a new sharp approximation for the gamma function via the tri-gamma function. This approximation is fast in comparison with the recently discovered asymptotic series. We also establish the inequalities related to this approximation. Finally, some numerical computations are provided for demonstrating the superiority of our approximation.
متن کاملSteins method, Malliavin calculus and infinite-dimensional Gaussian analysis
This expository paper is a companion of the four one-hour tutorial lectures given in the occasion of the special month Progress in Steins Method, held at the University of Singapore in January 2009. We will explain how one can combine Steins method with Malliavin calculus, in order to obtain explicit bounds in the normal and Gamma approximation of functionals of in nite-dimensional Gaussian ...
متن کاملVariance-Gamma and Monte Carlo
The Variance-Gamma (VG) process was introduced by Dilip B. Madan and Eugene Seneta as a model for asset returns in a paper that appeared in 1990, and subsequently used for option pricing in a 1991 paper by Dilip and Frank Milne. This paper serves as a tutorial overview of VG and Monte Carlo, including three methods for sequential simulation of the process, two bridge sampling methods, variance ...
متن کاملVariance Estimation in Nonparametric Regression via the Difference Sequence Method
Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence rates that are uniform over broad functional classes and bandwidths are fully characterized, and asymptotic normality is also established. We also show that for ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 2014
ISSN: 1083-6489
DOI: 10.1214/ejp.v19-3020