A strong approximation for double subfractional integrals

Abstract

A Riemann–Stieltjes integral strong approximation to double Stratonovich integrals with respect to odd and even fractional Brownian motions is considered. We prove the convergence in quadratic mean, uniformly on compact time intervals, of the ordinary double integral process obtained by linear interpolation of the odd and even fractional Brownian motions, to the double Stratonovich integral. The deterministic integrands are continuous or are given by bimeasures.

Keywords:

• Odd fractional Brownian motion
• Even fractional Brownian motion
• Double Stratonovich integral
• Approximation
• Wong–Zakai
• AMS 2000 Subject Classification
• 60H05

Acknowledgement

We acknowledge support from the Romanian Ministry of Education and Research (CEEX Program, Project 2-CEx06-11-18/2006). The author thanks the referees for careful reading and suggestions.