强化随机过程网络：一阶渐近学的完整描述

IF 1.1 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications Pub Date : 2024-07-06 DOI:10.1016/j.spa.2024.104427

Giacomo Aletti , Irene Crimaldi , Andrea Ghiglietti

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引用次数: 0

摘要

我们考虑了一组有限的强化随机过程，这些过程之间具有基于网络的一般交互作用。我们为出现某种形式的几乎确定的渐近同步提供了充分和必要的条件。具体来说，我们确定了三种情况：第一种情况涉及完全同步，即所有过程都向同一随机变量收敛；第二种情况显示系统几乎确定收敛，但不存在任何形式的同步；第三种情况显示在相互作用矩阵的循环类中存在几乎确定的渐近同步，同时这些类之间存在渐近周期行为。

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Networks of reinforced stochastic processes: A complete description of the first-order asymptotics

We consider a finite collection of reinforced stochastic processes with a general network-based interaction among them. We provide sufficient and necessary conditions for the emergence of some form of almost sure asymptotic synchronization. Specifically, we identify three regimes: the first involves complete synchronization, where all processes converge towards the same random variable; the second exhibits almost sure convergence of the system, but no form of synchronization subsists; and the third reveals a scenario where there is almost sure asymptotic synchronization within the cyclic classes of the interaction matrix, together with an asymptotic periodic behavior among these classes.

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来源期刊

Stochastic Processes and their Applications 数学-统计学与概率论

CiteScore

2.90

自引率

7.10%

发文量

180

审稿时长

23.6 weeks

期刊介绍： Stochastic Processes and their Applications publishes papers on the theory and applications of stochastic processes. It is concerned with concepts and techniques, and is oriented towards a broad spectrum of mathematical, scientific and engineering interests. Characterization, structural properties, inference and control of stochastic processes are covered. The journal is exacting and scholarly in its standards. Every effort is made to promote innovation, vitality, and communication between disciplines. All papers are refereed.