Wiener path intersections and local time
Journal Article
We study intersection properties of Wiener processes in the plane. For each positive integer k we show that k independent Wiener processes intersect almost surely in a set of Hausdorff dimension two, and that the set of points a single process visits at least k distinct times also has dimension two. We construct a functional on configurations of k independent Wiener processes that measures the extent to which the trajectories of the k processes intersect. We prove certain Lp estimates for this functional and show that it is a local time for a certain vector-valued multiparameter stochastic process. © 1978.
Full Text
Duke Authors
Cited Authors
- Wolpert, RL
Published Date
- January 1, 1978
Published In
Volume / Issue
- 30 / 3
Start / End Page
- 329 - 340
Electronic International Standard Serial Number (EISSN)
- 1096-0783
International Standard Serial Number (ISSN)
- 0022-1236
Digital Object Identifier (DOI)
- 10.1016/0022-1236(78)90061-7
Citation Source
- Scopus