Phase States Aggregation of Random Walk on a Multidimensional Lattice

IF 0.2 Q4 MATHEMATICS

Moscow University Mathematics Bulletin Pub Date : 2024-05-13 DOI:10.3103/s0027132224700074

G. A. Popov, E. B. Yarovaya

引用次数: 0

Abstract

A time-continuous random walk on a multidimensional lattice which underlies the branching random walk with an infinite number of phase states is considered. The random walk with a countable number of states can be reduced to a system with a finite number of states by aggregating them. The asymptotic behavior of the residence time of the transformed system in each of the states depending on the lattice dimension under the assumption of a finite variance and under the condition leading to an infinite variance of jumps of the original system is studied. It is shown that the aggregation of states in terms of the described process leads to the loss of the Markov property.

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多维晶格上随机漫步的相态聚合

摘要研究了多维网格上的时间连续随机行走，它是具有无限多个相态的分支随机行走的基础。具有可计状态数的随机游走可以通过聚集状态数简化为具有有限状态数的系统。在有限方差假设和导致原始系统跳跃方差无限的条件下，研究了变换后的系统在每个状态下停留时间的渐近行为，该时间取决于晶格维度。结果表明，根据所描述的过程聚集状态会导致马尔可夫特性的丧失。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Moscow University Mathematics Bulletin MATHEMATICS-

CiteScore

0.60

自引率

25.00%

发文量

期刊介绍： Moscow University Mathematics Bulletin is the journal of scientific publications reflecting the most important areas of mathematical studies at Lomonosov Moscow State University. The journal covers research in theory of functions, functional analysis, algebra, geometry, topology, ordinary and partial differential equations, probability theory, stochastic processes, mathematical statistics, optimal control, number theory, mathematical logic, theory of algorithms, discrete mathematics and computational mathematics.