FRACTIONAL BROWNIAN FIELDS OVER MANIFOLDS

被引：5
|
作者：
Gelbaum, Zachary A. [1 ]
机构：
[1] Oregon State Univ, Dept Math, Corvallis, OR 97331 USA
来源：
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2014年 / 366卷 / 09期
关键词：
HEAT KERNEL; STOCHASTIC-PROCESSES; RIEMANNIAN MANIFOLD; SPACES; BOUNDS; MOTION;
D O I：
10.1090/S0002-9947-2014-06106-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Extensions of the fractional Brownian fields are constructed over a complete Riemannian manifold. This construction is carried out for the full range of the Hurst parameter alpha epsilon (0, 1). In particular, we establish existence, distributional scaling (self-similiarity), stationarity of the increments, and almost sure Holder continuity of sample paths. Stationary counterparts to these fields are also constructed.
引用
收藏
页码：4781 / 4814
页数：34
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