The indeterminate rate problem for birthdeath processes
Doorn, Erik A. van (1987) The indeterminate rate problem for birthdeath processes. Pacific Journal of Mathematics, 130 (2). pp. 379393. ISSN 00308730

PDF
1MB 
Abstract:  A birthdeath process is completely determined by its set of rates if and only if this set satisfies a certain condition C, say. If for a set of rates R the condition C is not fulfilled, then the problem arises of characterizing all birthdeath processes which have rate set R (the indeterminate rate problem associated with R). We show that the characterization may be effected by means of the decay parameter, and we determine the set of possible values for the decay parameter in terms of JR. A fundamental role in our analysis is played by a duality concept for rate sets, which, if the pertinent rate sets satisfy C, obviously leads to a duality concept for birthdeath processes. The latter can be stated in a form which suggests the possibility of extension in the context of indeterminate rate problems. This, however, is shown to be only partially true. 
Item Type:  Article 
Additional information:  Open access 
Copyright:  © 1987 University of California Press 
Faculty:  Electrical Engineering, Mathematics and Computer Science (EEMCS) 
Research Group:  
Link to this item:  http://purl.utwente.nl/publications/70377 
Official URL:  http://projecteuclid.org/euclid.pjm/1102690184 
Export this item as:  BibTeX EndNote HTML Citation Reference Manager 
Repository Staff Only: item control page