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