Some Properties of Bifractional Bessel Processes Driven by Bifractional Brownian Motion

Abstract EN

Let B=Bt1,…,Btdt≥0 be a d-dimensional bifractional Brownian motion and Rt=Bt12+⋯+Btd2 be the bifractional Bessel process with the index 2HK≥1.

The Itô formula for the bifractional Brownian motion leads to the equation Rt=∑i=1d∫0tBsi/RsdBsi+HKd−1∫0ts2HK−1/Rsds.

In the Brownian motion case K=1 and H=1/2, Xt≔∑i=1d∫0tBsi/RsdBsi, d≥1 is a Brownian motion by Lévy’s characterization theorem.

In this paper, we prove that process Xt is not a bifractional Brownian motion unless K=1 and H=1/2.

We also study some other properties and their application of this stochastic process.