On the convex hull of symmetric stable processes
On the convex hull of symmetric stable processes
复制标题
对称稳定过程的凸包
DOI：
10.1090/s0002-9939-2012-11128-1
复制
发表时间：
2010
影响因子：
0.5
通讯作者：
G. Last
中科院分区：
文献类型：
--
作者：
J. Kampf;G. Last
设α∈(1，2]和X是独立对称分量从0开始的Rd值α-稳定过程。我们考虑X所描述的路在区间[0，t]上的闭包ST及其凸包ZT。本文的第一个结果给出了ZT的某些平均混合体积的公式，特别是ZT的期望第一内禀体积的公式。第二个结果讨论了稳定香肠ZT+B(其中B是具有内点的任意凸体)的期望体积为t→0的渐近性。
Let α ∈ (1, 2] and X be an Rd-valued α-stable process with independent and symmetric components starting in 0. We consider the closure St of the path described by X on the interval [0, t] and its convex hull Zt. The first result of this paper provides a formula for certain mean mixed volumes of Zt and in particular for the expected first intrinsic volume of Zt. The second result deals with the asymptotics of the expected volume of the stable sausage Zt+B (where B is an arbitrary convex body with interior points) as t→ 0.