连续介质中受扰动接触模型的持久性

IF 0.4 4区 数学 Q4 STATISTICS & PROBABILITY
P. Sergey, Z. Elena
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引用次数: 0

摘要

局部灾害会导致物种灭绝吗?我们在本文中回答了这个问题。在论文[19]中,我们考虑了局部紧凑度量空间上与状态相关的出生率和死亡率的接触过程,并对确保存在不变度量的出生率和死亡率提出了有利条件。[19]中的一个关键条件是临界制度条件,即平均出生率和死亡率之间存在平衡。在本研究中,我们摒弃了临界条件,假设违反了平衡条件。这意味着所考虑的接触模型的相关函数的演变是由一个受(负)电势扰动的非局部卷积型算子决定的。我们证明,死亡率的局部峰值通常不会导致物种灭绝。我们证明,即使不存在临界条件,也存在一系列不变度量,这些度量可以用费曼-卡克公式来描述。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Persistence in Perturbed Contact Models in Continuum
Can a local disaster lead to extinction? We answer this question in this work. In the paper [19] we considered contact processes on locally compact metric spaces with state dependent birth and death rates and formulated suf- ficient conditions on the rates that ensure the existence of invariant measures. One of the crucial conditions in [19] was the critical regime condition, which meant the existence of a balance between birth and death rates in average. In the present work, we reject the criticality condition and suppose that the bal- ance condition is violated. This implies that the evolution of the correlation functions of the contact model under consideration is determined by a nonlocal convolution type operator perturbed by a (negative) potential. We show that local peaks in mortality do not typically lead to extinction. We prove that a family of invariant measures exists even without the criticality condition and these measures can be described using the Feynman-Kac formula.
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来源期刊
Markov Processes and Related Fields
Markov Processes and Related Fields STATISTICS & PROBABILITY-
CiteScore
0.70
自引率
0.00%
发文量
0
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.
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