arXiv subjects
Publications and source records attributed to Elena Bashtova.
We consider a Jackson network with regenerative input flows in which every server is subject to a random environment influence generating breakdowns and repairs. They occur in accordance with two independent sequences of i.i.d. random variables. We establish a theorem on the strong approximation of the vector of queue lengths by a reflected Brownian motion in positive orthant.
This paper is a continuation of work arXiv:2006.09583 devoted to establishment of the convergence rate in the strong invariance principle for cumulative processes. We establish optimal rate of convergence for the case when regeneration periods and increments over them have only power moments of order greater than 2. Under this power-type conditions two types of approximation by Wiener process are proved: the rate of convergence in the Strassen's invariance principle and inequalities for the probability that random process deviates from the approximating one.
We establish optimal logarithmic rates of convergence in the strong invariance principle for multivariate cumulative processes in the Smith's sense. Exponential probabilistic inequalities of Komlós-Major-Tusnády type are obtained. Provided examples include applications to stopped sums and birth and death processes.