On the distribution of storage processes from the class \(V(\varphi,\psi)\). (English. Russian original) Zbl 1241.90009

Yamnenko, R. E.; Shramko, O. S.

Theory Probab. Math. Stat. 83, 191-206 (2011); translation from Teor. Jmovirn. Mat. Stat. 83, 163-176 (2010).

Summary: Estimates for the distribution of a storage process \[ Q(t)=\sup_{s\leq t}\big (X(t)-X(s)-(f(t)-f(s))\big) \] are obtained in the paper, where \( (X(t),t\in T)\) is a stochastic process belonging to the class \( V(\varphi ,\psi )\) and where the service output rate \( f(t)\) is a continuous function. In particular, the results hold if \( (X(t),t\in T)\) is a Gaussian process. Several examples of applications of the results obtained in the paper are given for sub-Gaussian stationary stochastic processes.

MSC:

90B05	Inventory, storage, reservoirs
60G07	General theory of stochastic processes
60K25	Queueing theory (aspects of probability theory)

Keywords:

metric entropy; queue; storage process; estimate of a distribution; sub-Gaussian process

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