Interacting Catalytic Feller Diffusions

Finite System Scheme and Renormalisation

By (author) Christian Penssel

Book cover: Interacting Catalytic Feller Diffusions

Extent: 295, 295 pages

Publisher: Logos Verlag Berlin

Subjects: Technical Sciences: Computer Science, Engineering, IT, & Math

Language: English

(Paperback) (Published)

(April 2004)

ISBN: 9783832505288

5.71 x 8.27 inches

Price: $61.00

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Synopsis
Contributing Authors

In dieser Dissertation werden katalytisch interagierende Fellersche Diffusionen untersucht. Der betrachtete Prozess ist ein katalytisches Zweitypenmodell; er wird definiert als Losung eines abzahlbaren Systems stochastischer Differentialgleichungen.Die Betrachtungen umfassen folgende Punkte:1. Zunachst wird das Langzeitverhaltens auf den unendlichen Gittern analysiert. Hier ist insbesondere der sogenannte Reaktantprozess von Interesse, da nicht a priori klar ist, in welcher Form sich hier die dimensionsabhangige Dichotomie des Langzeitverhaltens des Katalysten niederschlagt.2. Es wird ein dem 1990 von Cox und Greven eingefuhrten “Finite System Scheme” entsprechendes Theorem bewiesen. Im Mittelpunkt steht das Verhalten des Prozesses auf Tori im hochdimensionalen Fall. Es stellt sich heraus, dass im Limes grosser Systeme ein enger Zusammenhang besteht zwischen zeitreskaliertem Torussystem und den Gleichgewichten der Gittersysteme.3. Schliesslich wird die hierarchische Gruppe als zugrundeliegende raumliche Struktur gewahlt. Der 1993 von Dawson und Greven eingefuhrten “Multiple Space Time Scale Analysis” entsprechend wird auch hier unter Verwendung verschiedener Skalierungen der Zeit der Limes grosser Systeme betrachtet. Eine entscheidende Rolle kommt der sogenannten Wechselwirkungskette zu; sie beschreibt, wie die betrachteten hierarchischen Ebenen einander beeinflussen.

By (author) Christian Penssel

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