摘要: 设
为一维
-稳定模型且
。本文主要研究如下线性自排斥扩散的长时间行为和参数估计：
，其中
、
是两个未知参数且
。当
且
t趋于无穷大时，对任意
，我们有
和
几乎处处成立，其中
。在连续观测条件下，建立
和
的最小二乘估计讨论其相合性与渐近分布。
Abstract:
Let
be an
-stable motion of one-dimension with
. In this paper, we consider large time behaviors and parameter estimation of the linear self-repelling diffusion of the forms
where
and
are two unknown parameters. When
and
t tends to infinity, we show that the convergence
and
hold almost surely for all
, where
. The least squares estimates of
and
are established to discuss their coincidence and asymptotic distributions under continuous observation conditions.