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

Student
Title
Supervisor
Faculty
Educational Programme
Final Grade
Year of Graduation
Anastasiya Knutova
Asymptotics for Extrema of Steady State Distributions in Stochastic Models with Spatially Nonhomogeneous Dynamics
Faculty of Applied Mathematics and Cybernetics
Undergraduate programme
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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