Tsukuba Journal of Mathematics

Interactive infinite Markov particle systems with jumps

Seiji Hiraba

Full-text: Open access

Abstract

In [2] we investigated independent infinite Markov particle systems as measure-valued Markov processes with jumps, and we gave sample path properties and martingale characterizations. In particular, we investigated the exponent of Hölder-right continuity in case that the motion process is absorbing α-stable motion on (0,∞) with 0 < α < 2, that is, time-changed absorbing Brownian motions on (0,∞) by the increasing α/2-stable Lévy processes.In the present paper we shall extend the results to the case of simple interactive infinite Markov particle systems. We also consider the absorbing stable motion on a half space H = Rd−1 × (0,∞) as a motion process.

Article information

Source
Tsukuba J. Math., Volume 37, Number 1 (2013), 27-50.

Dates
First available in Project Euclid: 15 July 2013

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1373893404

Digital Object Identifier
doi:10.21099/tkbjm/1373893404

Mathematical Reviews number (MathSciNet)
MR3112417

Zentralblatt MATH identifier
1270.60057

Subjects
Primary: 60G57: Random measures
Secondary: 60G75

Keywords
particle systems measure-valued processes jump processes

Citation

Hiraba, Seiji. Interactive infinite Markov particle systems with jumps. Tsukuba J. Math. 37 (2013), no. 1, 27--50. doi:10.21099/tkbjm/1373893404. https://projecteuclid.org/euclid.tkbjm/1373893404


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