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Shock processes with aftereffects and multivariate lack of memory. (English) Zbl 0553.60078
The ’multivariate lack of memory’ functional equation, of which the Marshall-Olkin multivariate exponential distribution is the only solution under the requirement of exponential marginals, is reconsidered. The authors show that while the above functional equation, without the exponential marginals condition, has many solutions, the class of possible marginals is somewhat limited and not entirely free. A representation of the general solution of the multivariate lack of memory equation is obtained. Some examples from models of dependence leading to shock models with aftereffects are considered.
Reviewer: M.C.Bhattacharjee

MSC:
60K10 Applications of renewal theory (reliability, demand theory, etc.)
39B99 Functional equations and inequalities
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