MARKOV CHAINS AND RANDOM WALKS

Missouri Journal of Mathematical Sciences

We present a class of "nice" n × n finite Markov probability transition matrices and infinitesimal generators whose limiting (steady state) probabilities are proportional to the first n Fibonacci numbers. We extend this model to other sequences and discover some curious matrix and sequence relationships.

This paper examines conditions for recurrence and transience for ran-dom walks on discrete surfaces, such as Zd, trees, and random environ-ments. ... Definition 1. A class of subsets F of a set Ω is an algebra if the following hold: ... 2. A1,A2,...,An ∈ F =⇒ ⋃n i=1 Ai ∈ F. 3. ...

The Mathematical Intelligencer, 2022

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Journal of Applied Logic, 2016

Logical theories have been developed which have allowed temporal reasoning about eventualities (a la Galton) such as states, processes, actions, events, processes and complex eventualities such as sequences and recurrences of other eventualities. This paper presents the problem of coincidence within the framework of a first order logical theory formalizing temporal multiple recurrence of two sequences of fixed duration eventualities and presents a solution to it The coincidence problem is described as: if two complex eventualities (or eventuality sequences) consisting respectively of component eventualities x 0 , x 1 ,....,x r and y 0 , y 1 , ..,y s both recur over an interval k and all eventualities are of fixed durations, is there a subinterval of k over which the incidence x t and y u for 0 t  r and 0  u  s coincide. The solution presented here formalizes the intuition that a solution can be found by temporal projection over a cycle of the multiple recurrence of both sequences.

Lecture Notes in Computer Science, 2006

Journal of Mathematical Physics, 1999

A reinforced random walk on the d-dimensional lattice is considered. It is shown that this walk is equivalent to an iterated function system ͑IFS͒. Criteria for the existence of limit cycles are given. Numerical results and conjectures about the quantitative behavior of the walk are stated.

Mathematics

Probability resembles the ancient Roman God Janus since, like Janus, probability also has a face with two different sides, which correspond to the metaphorical gateways and transitions between the past and the future[...]

International Journal of Mathematics Trends and Technology, 2014

When introducing sequences to students, the first skill we teach them is how to predict the next term of a sequence given the first few terms, usually the first three, four or five terms. In this note, we intend to show that given some terms of a sequence, the next term is not uniquely determined in most cases. We will also show under which condition can the next term be determined uniquely.