Research Reports from the Department of Operations
Document Type
Dissertation
Publication Date
6-1-1972
Abstract
The following result is proved: For any given continuous function and any T > 0, the set of points between zero and T where the sample path of a standard separable Brownian motion process intersects the graph of the function is almost surely either a perfect set or a set which is perfect if the origin is removed. Sufficient conditions are given for that set to be perfect and sufficient conditions are given for it to be perfect if the origin is removed.
Keywords
Operations research, Brownian motion processes, Stochastic processes, Set theory, Mathematical analysis
Publication Title
Dissertation/Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University
Issue
Technical memorandum no. 184 ; Submitted in partial fulfillment of the requirements for the Degree of Doctor of Philosophy.
Rights
This work is in the public domain and may be freely downloaded for personal or academic use
Recommended Citation
Rowland, Douglas Yates, "Crossings of Curves by a One-Dimensional Brownian Motion Process" (1972). Research Reports from the Department of Operations. 120.
https://commons.case.edu/wsom-ops-reports/120