Asymptotics for Extrema of Steady State Distributions in Stochastic Models with Spatially Nonhomogeneous Dynamics

Student: Knutova Anastasiya

Faculty: Faculty of Applied Mathematics and Cybernetics

Educational Programme: Specialist

Year of Graduation: 2014

We consider a birth-death process with N states where N is finite but arbitrarily large.          We assume that transition rates are piecewise constant functions of states.We found a steady state distribution for any  N.  For all parameter’s values we found maximum and minimum stationary probabilities.We study an asymptotic behavior of the maximum and minimum stationary probabilities as N becomes arbitrarily large.We find the main term in the asymptotic of the maximum and minimum components of the steady state distribution.

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