具有多项式速率的对称生死过程的融合近似法

IF 0.4 4区数学 Q4 STATISTICS & PROBABILITY

Markov Processes and Related Fields Pub Date : 2024-01-02 DOI:10.61102/1024-2953-mprf.2023.29.4.007

A. Logachov, O. Logachova, E. Pechersky, E. Presman, A. Yambartsev

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引用次数: 0

摘要

本文研究了在非负整数 x∈Z + 上以多项式速率 x α , α∈ [1, 2], x 6= 0 的对称出生和死亡随机过程。该过程移动缓慢，在状态 0 附近停留的时间较长。我们证明了缩放过程对无漂移随机二阶方程解的收敛性。在极限过程中会出现粘滞现象：从任何状态出发的轨迹都需要花费有限的时间到达 0，并无限地停留在那里。

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

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.

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来源期刊

Markov Processes and Related Fields STATISTICS & PROBABILITY-

CiteScore

0.70

自引率

0.00%

发文量

期刊介绍： Markov Processes And Related Fields The Journal focuses on mathematical modelling of today''s enormous wealth of problems from modern technology, like artificial intelligence, large scale networks, data bases, parallel simulation, computer architectures, etc. Research papers, reviews, tutorial papers and additionally short explanations of new applied fields and new mathematical problems in the above fields are welcome.