Diffusion Approximation for Symmetric Birth-and-Death Processes with Polynomial Rates
A. V. Logachov, O. Logachova, E.A. Pechersky, E.L. Presman, A.A. Yambartsev
2023, v.29, Issue 4, 605-618
ABSTRACT
The symmetric birth and death stochastic process on the non-negative integers x^α, α ∈ [1, 2], x non equal to 0 with polynomial rates $x^\alpha, \alpha \in [1,2], x\ne 0$, is studied. The process moves slowly and spends more time in the neighborhood of the state 0. We prove the convergence of the scaled process to a solution of stochastic differential equation without drift. Sticking phenomenon appears at the limiting process: trajectories, starting from any state, take finite time to reach 0 and remain there indefinitely.
DOI:
10.61102/1024-2953-mprf.2023.29.4.007
Keywords: birth-death processes, stochastic differential equations, diffusion approximation
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