12
월
23
일
(
오후
4
시
)
제목
:
Some stability properties of a reflected fractional Brownian motion on the positive orthant
발표자
:
이치훈 교수님
(
콜로라도 주립대 통계학과
)
발표내용
: We consider a multidimensional reflected fractional Brownian motion process (rfBm) on the positive orthant with drift and Hurst parameter 1/2<H<1. Motivation for studying such processes stems from the fact that rfBm appears as a limiting workload process for fluid queueing network models fed by a large number of heavy tailed ON/OFF sources in heavy traffic. Under a natural stability condition on the drift vector and reflection directions, we show uniform return time results to some compact sets hold. Also, under slightly stronger stability assumptions, we establish a geometric drift towards a compact set for the 1-skeleton rfBm chain. These results can be viewed as steps towards the further analysis of rfBm with the aim of establishing recurrent properties for reflected processes driven by non-Markovian processes.