Transient detailed balance and product form for reaction networks. Issue 2 (3rd April 2017)

• Record Type: Journal Article
• Authors: den Boer, Arnoud V.; Boucherie, Richard J.
• Is Part Of: Stochastic models. Volume 33:Issue 2(2017)
• Page Start: 322
• Page End: 341
• Publication Date: 2017-04-03
• Subjects: Clustering process -- linear system -- queueing network -- transient behavior; Primary: 60J27 -- Secondary: 60K25; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/15326349.2017.1286510
• Languages: English
• ISSNs: 1532-6349

Abstract

ABSTRACT: This paper explores the boundary of the set of reaction networks that have an exact transient (truncated) multidimensional Poisson or product-form distribution for the number of particles of different types. Motivated by the birth–death process, we introduce the notions of transient detailed balance and delay functions, and use these notions to obtain the novel transient product-form distribution in a coagulation-fragmentation process for polymers with a tree-like structure from that of the pure coagulation process.