Non symmetric Rosenblatt process over a compact

Abstract

In this short note, we give the representation of the non symmetric Rosenblatt process as a Wiener–Itô multiple integral with respect to the Brownian motion on a finite interval. Based on this representation, we obtain a least square-type estimator for an unknown parameter of the drift coefficient of a simple model driven by the non symmetric Rosenblatt process.

Keywords:

• Least square estimation
• non symmetric Rosenblatt process
• self-similarity
• Wiener chaos

2010 AMS Classification Numbers:

• 60G18
• 60G12
• 62M86

Additional information

Funding

Héctor Araya was partially supported by MATH-AmSud 18-MATH-07 SaSMoTiDep Project and Proyecto Fondecyt Post-Doctorado, Chile 3190465. Johanna Garzón is partially supported by MATH-AmSud 18-MATH-07 SaSMoTiDep Project and HERMES project 41305. Tania Roa was partially supported by Beca CONICYT-PFCHA/Doctorado Nacional/2018-21180298. Fondo de Fomento al Desarrollo Científico y Tecnológico