Homogeneity and the Strong Markov Property.
Abstract
The strong Markov property of a process X at a stopping time tau may be split into a conditional independence part (CI) and a homogeneity part (H). However, it turns out that (H) often implies at least some version of (CI). In the present paper, we shall assume that (H) holds on the set (X is a member of B) , for all stopping times tau such that X is a member of F a.s., where F is a closed recurrent subset of the state space S, while B is a proper subset of F. If F=S, then (CI) will hold on (X is a member of B) for every stopping time tau, so in this case X is regenerative in B. In the general case, the same statement is conditionally true in a suitable sense, given some shift invariant delta-field. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1985
- Accession Number
- ADA166221
Entities
People
- Olav Kallenberg
Organizations
- University of North Carolina at Chapel Hill