Related papers: Some notes on Lamperti's recurrence of stochastic …
We derive a general recurrence relation for squares of Fibonacci-like numbers. Various properties are developed, including double binomial summation identites.
We investigate the properties of chain recurrent, chain transitive, and chain mixing maps (generalizations of the well-known notions of non-wandering, topologically transitive, and topologically mixing maps). We describe the structure of…
On the topic of probabilistic rewriting, there are several works studying both termination and confluence of different systems. While working with a lambda calculus modelling quantum computation, we found a system with probabilistic…
In this note we provide a simple formula of general term of recurrent sequence.
We use Grothendieck theorem to prove a structure theorem for multicorrelation sequences of length two, associated with two (not necessarily commuting) measure preserving actions on a probability space. We use this to deduce a multiple…
This paper investigates stochastic finite matrices and the corresponding finite Markov chains constructed using recurrence matrices for general families of orthogonal polynomials and multiple orthogonal polynomials. The paper explores the…
We consider Markov chains on partially ordered sets that generalize the success-runs and remaining life chains in reliability theory. We find conditions for recurrence and transience and give simple expressions for the invariant…
Let $(a_n)_{n=0}^\infty$ be a second-order linear recurrence sequence with constant coefficients over the field of $p$-adic numbers $\mathbb{Q}_p$. We study the set of limit points of the sequence of consecutive ratios…
In this paper we propose a definition of a recurrence relation homomorphism and illustrate our definition with a few examples. We then define the period of a k-th order of linear recurrence relation and deduce certain preliminary results…
We show that essentially the Fibonacci sequence is the unique binary recurrence which contains infinitely many three-term arithmetic progressions. A criterion for general linear recurrences having infinitely many three-term arithmetic…
Recursive stochastic algorithms have gained significant attention in the recent past due to data driven applications. Examples include stochastic gradient descent for solving large-scale optimization problems and empirical dynamic…
We prove a number of conjectures [arXiv:2005.04066] recently stated by P. Barry, related to the paperfolding sequence and the Rueppel sequence.
We derive the conditions for recurrence and transience for time-inhomogeneous birth-and-death processes considered as random walks with positively biased drifts. We establish a general result, from which the earlier known particular results…
Modifying an idea of E. Brietzke we give simple proofs for the recurrence relations of some sequences of binomial sums which have previously been obtained by other more complicated methods.
This work is a continuation of [Kalikaeva, MPRF, 23(2):225-240]. The object of study is ``Markov-up processes'' on $\mathbb Z_+$ and the moment of downcrossing a certain barrier. The processes considered in this paper differ from Markov…
In order to simulate observational and experimental situations, we consider a leak in the phase space of a chaotic dynamical system. We obtain an expression for the escape rate of the survival probability applying the theory of transient…
We study the recurrence of the product of n functions, each of which satisfies the same recurrence relation.
The Lamperti transform offers a powerful bridge between self-similar processes and stationary dynamics, making it especially useful for analyzing anomalous diffusion models that lack stationary increments. In this paper we examine the…
Due to some results by John P. D Angelo and Dusty Grundmeier about CR- mappings the main results of my 2001 paper about recurrences for some sequences of binomial sums can be simplified.
In this article we define a minor relation, which is stronger than the classical one, but too strong to become a well-quasi-order on the class of finite graphs. Nevertheless, with this terminology we are able to introduce a conjecture,…