Limit theorems and structural properties of the cat-and-mouse markov chain and its generalisations

Sergey Foss, Timofei Prasolov, Seva Shneer

Результат исследования: Научные публикации в периодических изданияхстатьярецензирование

Аннотация

We revisit the so-called cat-and-mouse Markov chain, studied earlier by Litvak and Robert (2012). This is a two-dimensional Markov chain on the lattice <![CDATA[ $\mathbb{Z}^2$ ]]>, where the first component (the cat) is a simple random walk and the second component (the mouse) changes when the components meet. We obtain new results for two generalisations of the model. First, in the two-dimensional case we consider far more general jump distributions for the components and obtain a scaling limit for the second component. When we let the first component be a simple random walk again, we further generalise the jump distribution of the second component. Secondly, we consider chains of three and more dimensions, where we investigate structural properties of the model and find a limiting law for the last component.

Язык оригиналаанглийский
Страницы (с-по)141-166
Число страниц26
ЖурналAdvances in Applied Probability
Том54
Номер выпуска1
DOI
СостояниеОпубликовано - 28 мар. 2022

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