Ultrametric Matrices and Induced Markov Chains

✍ Scribed by Claude Dellacherie; Servet Martı́nez; Jaime San Martı́n

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 214 KB
• Volume: 17
• Category: Article
• ISSN: 0196-8858
• DOI: 10.1006/aama.1996.0009

✦ Synopsis

We study non-singular ultrametric matrices A. These kinds of matrices are restrictions of non-singular tree matrices. The structure of A y1 allows us to associate to A some substochastic kernels P. We are able to describe the graph of P, in particular those vertices which lose mass. Our main tools are an algebraic decomposition lemma of A y1 and the study of the minimal tree matrix associated to A.