Boundaries from inhomogeneous Bernoulli trials

TL;DR

This paper investigates the boundary problem for inhomogeneous increasing random walks on a lattice, providing explicit solutions for specific cases linked to classical and generalized number triangles.

Contribution

It offers explicit solutions to the boundary problem for inhomogeneous Bernoulli trials on a lattice, extending classical number triangle concepts.

Findings

Explicit solutions for boundary problems in specific inhomogeneous Bernoulli models

Connections established between boundary solutions and classical number triangles

Enhanced understanding of inhomogeneous random walk boundaries

Abstract

The boundary problem is considered for inhomogeneous increasing random walks on the square lattice ${\mathbb Z}_+^2$ with weighted edges. Explicit solutions are given for some instances related to the classical and generalized number triangles.