Some path properties of weighted-fractional Brownian motion

Abstract

In this paper we consider the weighted-fractional Brownian motion with indexes a, b () and narrow the focus to obtain some properties of sample paths. Motivated by the asymptotic property

for all s>0, we consider the -strong variation of the principal value type defined by the limit

with for all t>0, where the limits are uniform in probability on each compact interval. We show that is strongly locally -non-deterministic with , and by applying this property we study Chung's law of the iterated logarithm for and intersection local time on .

Keywords::

• weighted-fractional Brownian motion
• strong local non-determinism
• α-strong variation
• the collision local time and the iterated logarithm

MSC (2010) Classification::

• 60G15
• 60G17
• 60G22

Additional information

Funding

This project is sponsored by NSFC [grant number 11171041, 11201062]; Innovation Program of Shanghai Municipal Education Commission [grant number 12ZZ063]; the Research Project of Education of Zhejiang Province (Y201326507); the Fundamental Research Funds for the Central Universities.