Variable Length Markov Chains, Persistent Random Walks: a close encounter

TL;DR

This paper explores the relationship between random walks and Variable Length Markov Chains, focusing on their semi-Markov properties to understand their connection and differences.

Contribution

It provides a detailed analysis of how VLMCs relate to random walks through the lens of semi-Markov processes, bridging two research areas.

Findings

Identifies the semi-Markov property as a key link between VLMCs and random walks.

Clarifies the structural differences and similarities between the two models.

Offers insights into modeling complex stochastic processes using VLMCs.

Abstract

This is the story of the encounter between two worlds: the world of random walks and the world of Variable Length Markov Chains (VLMC). The meeting point turns around the semi-Markov property of underlying processes.