The Fractal Character of Localizable Measure-Valued Processes. I — Random Measures on Product Spaces

✍ Scribed by U. Zähle

• Publisher: John Wiley and Sons
• Year: 1988
• Tongue: English
• Weight: 386 KB
• Volume: 136
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19881360110

✦ Synopsis

In part II the evolation of large popnfationa of infinitesimal particles is stadied, in which one can follow the path of m y particle snfviviag up to bime t. To construct the diatribution of the totality of these pathsthe so-called backward tree -, we need a general extension theorem for random measures. The present port gives such a theorem under very ndxral conditions, and ita variante for product spaces. Measure-valued random processes are of increasing interest, since they arise in a variety of theoretical and applied settings, mentioned e.g. in 141. As a special class, Z --T Iim pt-b 3 v;f(r, 00) > 0 . c But this is a contrildiction to U, J 0 , and so (M 2) holds. I Relerences [ 11 D. A. DAWSON, The critical measure diffusion process, 2. Wahrscheinlichkeitstheorie verw.