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A classification of storage processes with stable input and output function. (English. Ukrainian original) Zbl 0943.60099

Theory Probab. Math. Stat. 52, 81-89 (1996); translation from Teor. Jmovirn. Mat. Stat. 52, 77-85 (1995).
The author finds necessary and sufficient conditions for the existence of stationary distribution, recurrence and existence of local time at zero for the storage process \(dX_t=dA_t-r(X_t)dt,\) where \(A_t\) is a nondecreasing homogeneous process with independent increments (input), \(r(x)\) is a nonnegative function (output function): \(r(x)=x^{\beta}\), \(\beta\geq 0\), \(E\exp\{-sA_t\}=\exp\{-t\int_0^{\infty} (1- \exp(-su))\nu(du)\}\), \(\nu(du)=cu^{-1-\alpha} du\), \(0<\alpha<1\), \(c>0.\)

MSC:

60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
60G52 Stable stochastic processes
60J55 Local time and additive functionals
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