Probability distribution of constrained Random Walks

TL;DR

This paper analyzes the limiting distribution of a dependent sequence of coin tosses using the method of images, providing insights into non-i.i.d. stochastic processes.

Contribution

It introduces a novel application of the method of images to compute the limiting distribution of constrained dependent coin toss sequences.

Findings

Derived the limiting distribution for the dependent coin toss sequence.

Demonstrated the effectiveness of the method of images in non-i.i.d. contexts.

Provided a mathematical framework for analyzing constrained random walks.

Abstract

In this paper we consider a sequence of n coin tosses, whose outcome depends on the previous n-1 tosses. In particular, their distribution is not i.i.d. We compute the limiting distribution of this sequence using the method of images.