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Stochastic order and martingale dynamics in multivariate life length models: A review. (English) Zbl 0762.60079
Stochastic orders and decision under risk, Proc. Int. Workshop, Hamburg/Ger. 1989, IMS Lect. Notes, Monogr. Ser. 19, 7-24 (1991).
[For the entire collection see Zbl 0745.00058.]
Authors’ summary: The purpose of this paper is to review some ideas connected to aging and dependence, in the context of technical reliability. The dynamic aspects of these notions are stressed throughout. The review is based mainly on the authors’ own work in the past decade, but it connects very closely with some recent results by the reviewer and J. G. Shanthikumar [Stochastic Processes Appl. 24, 241-258 (1987; Zbl 0622.60023); Adv. Appl. Probab. 19, 123-137 (1987; Zbl 0621.60096); Math. Oper. Res. 15, No. 3, 545-552 (1990; Zbl 0714.60078)]. New definitions, results and examples are also presented.
Reviewer: M.Shaked (Tucson)

60K10 Applications of renewal theory (reliability, demand theory, etc.)
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60K99 Special processes
60G44 Martingales with continuous parameter