On intensities of modulated Cox measures

[摘要] In this paper we introduce and study functionals of the intensities of random measures modulated by a stochastic processξ, which occur in applications to stochastic models and telecommunications. Modulation of a random measure byξis specified for markedCoxmeasures. Particular cases of modulation byξas semi-Markov and semiregenerative processes enabled us to obtain explicit formulas for the named intensities. Examples in queueing (systems with state dependent parameters, Little's and Campbell's formulas) demonstrate the use of the results.

[学科分类] 应用数学