Translator Disclaimer
2019 Necessary and sufficient conditions for limit theorems for quadratic variations of Gaussian sequences
Lauri Viitasaari
Probab. Surveys 16(none): 62-98 (2019). DOI: 10.1214/15-PS267

Abstract

The quadratic variation of Gaussian processes plays an important role in both stochastic analysis and in applications such as estimation of model parameters, and for this reason the topic has been extensively studied in the literature. In this article we study the convergence of quadratic sums of general Gaussian sequences. We provide necessary and sufficient conditions for different types of convergence including convergence in probability, almost sure convergence, $L^{p}$-convergence as well as weak convergence. We use a practical and simple approach which simplifies the existing methodology considerably. As an application, we show how convergence of the quadratic variation of a given process can be obtained by an appropriate choice of the underlying sequence.

Citation

Download Citation

Lauri Viitasaari. "Necessary and sufficient conditions for limit theorems for quadratic variations of Gaussian sequences." Probab. Surveys 16 62 - 98, 2019. https://doi.org/10.1214/15-PS267

Information

Received: 1 October 2015; Published: 2019
First available in Project Euclid: 31 May 2019

zbMATH: 07064382
MathSciNet: MR3960291
Digital Object Identifier: 10.1214/15-PS267

Subjects:
Primary: 60G15
Secondary: 60F05, 60F15, 60F25

JOURNAL ARTICLE
37 PAGES


SHARE
Vol.16 • 2019
Back to Top