Related papers: Some notes on Lamperti's recurrence of stochastic …
We consider reversible random walks in random environment obtained from symmetric long--range jump rates on a random point process. We prove almost sure transience and recurrence results under suitable assumptions on the point process and…
The multitime multiple recurrences are common in analysis of algorithms, computational biology, information theory, queueing theory, filters theory, statistical physics etc. The theoretical part about them is little or not known. That is…
The theory of ``Markov-up'' processes is being developed. This is a new class of stochastic processes with ``partial'' markovian features; it could also be called ``one-sided Markov''. Such a behavior may be found in the real world and in…
Recently E. Bombieri and N. M. Katz (2010) have demonstrated that several well-known results about the distribution of values of linear recurrence sequences lead to interesting statements for Frobenius traces of algebraic curves. Here we…
We introduce the notion of recurrence and transience for graphs over non-Archimedean ordered field. To do so we relate these graphs to random walks of directed graphs over the reals. In particular, we give a characterization of the real…
We define recurrence matrices and study a few properties (links with automatic sequences, branch groups etc.) of them.
A classic and fundamental result about the decomposition of random sequences into a mixture of simpler ones is de Finetti's Theorem. In its original form it applies to infinite 0-1 valued exchangeable sequences. Later it was extended and…
Combinatorial interpretation of the fibonomial coefficients recently proposed by the present author results here in combinatorial interpretation of the recurrence relation for fibonomial coefficients . The presentation is provided with…
The present paper extends the earlier results obtained by Abramov [`Conditions for recurrence and transience for time-inhomogeneous birth-and-death processes' \emph{Bull. Aust. Math. Soc.} \textbf{109} (2024), 393--402] for the case of…
This paper is concerned with the concept of linear repetitivity in the theory of tilings. We prove a general uniform subadditive ergodic theorem for linearly repetitive tilings. This theorem unifies and extends various known (sub)additive…
In the first part of this thesis, we study a Markov chain on $\mathbb{R}_+ \times S$, where $\mathbb{R}_+$ is the non-negative real numbers and $S$ is a finite set, in which when the $\mathbb{R}_+$-coordinate is large, the $S$-coordinate of…
In the present paper, we propose a new generalization of the Borel-Cantelli lemma. This generalization can be further used to derive strong limit results for Markov chains. Illustrative applications are provided.
The purpose of this paper is twofold. First, the definition of new statistical convergence with Fibonacci sequence is given and some fundamental properties of statistical convergence are examined. Second, approximation theory worked as a…
We give a new proof of a lemma by L. Shepp, that was used in connection to random coverings of a circle.
In the paper, the author derives several "diagonal" recurrence relations, constructs some inequalities, finds monotonicity, and poses a conjecture related to Stirling numbers of the second kind.
In this article we characterise discrete time stationary fields by difference equations involving stationary increment fields and self-similar fields. This gives connections between stationary fields, stationary increment fields and,…
This note proposes a new proof and new perspectives on the so-called Elliptical Potential Lemma. This result is important in online learning, especially for linear stochastic bandits. The original proof of the result, however short and…
We establish general theorems quantifying the notion of recurrence --- through an estimation of the moments of passage times --- for irreducible continuous-time Markov chains on countably infinite state spaces. Sharp conditions of…
An analytical formula for the occurence probability of Markovian stochastic paths with repeatedly visited and/or equal departure rates is derived. This formula is essential for an efficient investigation of the trajectories belonging to…
In this work we study the asymptotic of renewal sequences associated with certain transient renewal Markov chains and enquire about the existence of limit laws in this set up.