A Local Time for a Storage Process.
Abstract
A storage system subject to a general release rule and an additive input process is considered. If (X sub t) is the content at time t, then the set X = X sub t; t> or = 0) is a standard Markov process, and the concern is the local time at x = 0 of this process X. Depending on the parameters of the system, namely the release rule and the Levy measure of the input process, there are four cases possible. In terms of the set E = (t : X sub t = 0), these are as follows: E is the union of countably many isolated points; E is the union of countably many disjoint intervals; E is a Cantor set (a perfect set with an empty interior) with positive Lebesgue measure; E is a Cantor set with Lebesgue measure zero. The last is the most interesting case, and the construction of the local time then is the main result. Local times in other cases are also considered along with time inverses and hitting times. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1972
- Accession Number
- AD0742347
Entities
People
- Erhan Cinlar
Organizations
- Stanford University