Limit theorems for quadratic variations of the Lei–Nualart process

Salwa Bajja, Khalifa Es-Sebaiy*, Lauri Viitasaari

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

Abstract

Let X be a Lei–Nualart process with Hurst index H∈(0,1), Z1 be an Hermite random variable. For any n ≥ 1, set (Formula Presented) The aim of the current paper is to derive, in the case when the Hurst index verifies H > 3/4, an upper bound for the total variation distance between the laws L(Zn) and L(Z1), where Zn stands for the correct renormalization of Vn which converges in distribution towards Z1. We derive also the asymptotic behavior of quadratic variations of process X in the critical case H=3/4, i.e. an upper bound for the total variation distance between the L(Zn) and the Normal law.

Original languageEnglish
Title of host publicationStochastic Processes and Applications - SPAS2017
EditorsSergei Silvestrov, Anatoliy Malyarenko, Milica Rančić
Pages105-121
Number of pages17
DOIs
Publication statusPublished - 1 Jan 2018
MoE publication typeA4 Article in a conference publication
EventInternational Conference on Stochastic Processes and Algebraic Structures – From Theory Towards Applications - Västerås and Stockholm, Sweden
Duration: 4 Oct 20176 Oct 2017

Conference

ConferenceInternational Conference on Stochastic Processes and Algebraic Structures – From Theory Towards Applications
Abbreviated titleSPAS
CountrySweden
CityVästerås and Stockholm
Period04/10/201706/10/2017

Keywords

  • Berry–Esseen bounds
  • Convergence in law
  • Gaussian analysis
  • Hermite random variable
  • Malliavin calculus

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