TY - JOUR

T1 - Diffusion Approximation for Symmetric Birth-and-Death Processes with Polynomial Rates

AU - Logachov, A.

AU - Logachova, O.

AU - Pechersky, E.

AU - Presman, E.

AU - Yambartsev, A.

N1 - AL and AY thank FAPESP for support under Grant 2022/01030-0 and 2017/10555-0. AL thanks IME, Universidade de Sao Paulo, for hospitality. AL is also supported by the Ministry of Science and Higher Education of the Russian Federation grant FWNF-2022-0010.

PY - 2023

Y1 - 2023

N2 - The symmetric birth and death stochastic process on the non-negative integers x ∈ Z + with polynomial rates x α , α ∈ [1, 2], x 6= 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.

AB - The symmetric birth and death stochastic process on the non-negative integers x ∈ Z + with polynomial rates x α , α ∈ [1, 2], x 6= 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.

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85200764957&origin=inward&txGid=28ffb33292b6e3c844ab4a6e8a36cbed

UR - https://www.mendeley.com/catalogue/54d8ae2a-3472-3b00-ad29-729cf6cc96f3/

U2 - 10.61102/1024-2953-mprf.2023.29.4.007

DO - 10.61102/1024-2953-mprf.2023.29.4.007

M3 - Article

VL - 29

SP - 605

EP - 618

JO - Markov Processes And Related Fields

JF - Markov Processes And Related Fields

SN - 1024-2953

IS - 4

ER -