Joint continuity and representations of additive functionals of d-dimensional Brownian motion
Joint continuity and representations of additive functionals of d-dimensional Brownian motion
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d维布朗运动的加性泛函的联合连续性和表示
DOI：
10.1016/0304-4149(84)90002-4
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发表时间：
1984
影响因子：
1.4
通讯作者：
R. Bass
中科院分区：
文献类型：
--
作者：
R. Bass
给出了测度族{μa，0 <$a <$1}的条件，使得d维布朗运动的可加泛函族{Aat，0 <$a <$1}在aandt，a.s.中联合连续.然后，这被用来给出对一维布朗运动有效的表示At = Δ Lytμ（dy）的ad维模拟，其中Lyt是局部时间aty。使用超平面上的本地时间代替点上的本地时间。
Conditions are given on a family of measures {μa, 0⩽a⩽1} so that the corresponding family {Aat, 0⩽a⩽1} of additive functionals ofd-dimensional Brownian motion will be jointly continuous inaandt, a.s. This is then used to give ad-dimensional analogue to the representationAt= ∝Lytμ(dy) that is valid for one-dimensional Brownian motion, whereLytis local time aty. In place of local times at points, local times at hyperplanes are used.