L2-convergence rate for the discretization error of functions of Lévy process

In this article, we investigate the -convergence rate for the discretization error of the Clark-Ocone representation of a random variable , where is a pure-jump Lévy process. As in the Brownian case, we find that the exact rate is subject to the Sobolev-differentiability index (in the sense of class...

Full description

Saved in:
Bibliographic Details
Published in:Stochastics (Abingdon, Eng. : 2005) Eng. : 2005), 2020-06, Vol.92 (4), p.566-594
Main Authors: Amaba, Takafumi, Nien-Lin, Liu, Makhlouf, Azmi, Saidaoui, Takwa
Format: Article
Language:eng ; jpn
Subjects:
Convergence
Discretization
Indexing
Random variables
Stochastic processes
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this article, we investigate the -convergence rate for the discretization error of the Clark-Ocone representation of a random variable , where is a pure-jump Lévy process. As in the Brownian case, we find that the exact rate is subject to the Sobolev-differentiability index (in the sense of classical Malliavin calculus) of the space to which belongs.
ISSN:1744-2508
1744-2516
DOI:10.1080/17442508.2019.1642338