Extrema of Stationary Distributions for Stochastic Models with Large Number of States

Student: Razheva Anastasiya

Faculty: Faculty of Applied Mathematics and Cybernetics

Educational Programme: Specialist

Year of Graduation: 2014

In this work a homogeneous Markov process is studied.  The state graph of this process consists of two connected binary trees.  The first tree has N1 levels and the second tree has N2 levels. N1 and N2 can be arbitrary large.We consider two cases: N1=N2 and N1 is proportional to N2. We want to study the long term behavior of the process. We find a steady state distribution.   For all parameter’s values we find extrema of stationary distributions (maxima and minima). We find the main term in the asymptotics of the extrema of the stationary distribution as N1 and N2 increase without bound.

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