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Diffusion Approximation for Symmetric Birth-and-Death Processes with Polynomial Rates. / Logachov, A.; Logachova, O.; Pechersky, E. et al.

In: Markov Processes And Related Fields, Vol. 29, No. 4, 2023, p. 605-618.

Research output: Contribution to journal › Article › peer-review

Harvard

Logachov, A, Logachova, O, Pechersky, E, Presman, E & Yambartsev, A 2023, 'Diffusion Approximation for Symmetric Birth-and-Death Processes with Polynomial Rates', Markov Processes And Related Fields, vol. 29, no. 4, pp. 605-618. https://doi.org/10.61102/1024-2953-mprf.2023.29.4.007

APA

Logachov, A., Logachova, O., Pechersky, E., Presman, E., & Yambartsev, A. (2023). Diffusion Approximation for Symmetric Birth-and-Death Processes with Polynomial Rates. Markov Processes And Related Fields, 29(4), 605-618. https://doi.org/10.61102/1024-2953-mprf.2023.29.4.007

Vancouver

Logachov A, Logachova O, Pechersky E, Presman E, Yambartsev A. Diffusion Approximation for Symmetric Birth-and-Death Processes with Polynomial Rates. Markov Processes And Related Fields. 2023;29(4):605-618. doi: 10.61102/1024-2953-mprf.2023.29.4.007

Author

Logachov, A. ; Logachova, O. ; Pechersky, E. et al. / Diffusion Approximation for Symmetric Birth-and-Death Processes with Polynomial Rates. In: Markov Processes And Related Fields. 2023 ; Vol. 29, No. 4. pp. 605-618.

BibTeX

@article{5bce9bf9b4b745c2b68ea3fcd9bebf3b,
title = "Diffusion Approximation for Symmetric Birth-and-Death Processes with Polynomial Rates",
abstract = "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.",
author = "A. Logachov and O. Logachova and E. Pechersky and E. Presman and A. Yambartsev",
note = "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.",
year = "2023",
doi = "10.61102/1024-2953-mprf.2023.29.4.007",
language = "English",
volume = "29",
pages = "605--618",
journal = "Markov Processes And Related Fields",
issn = "1024-2953",
publisher = "Polymat",
number = "4",

}

RIS

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 -

ID: 60301207