On the Viterbi process with continuous state space

TL;DR

This paper investigates the convergence behavior of the Viterbi algorithm in hidden Markov models with continuous state spaces, revealing a stabilization phenomenon different from finite-state cases.

Contribution

It introduces a new understanding of the Viterbi process in continuous state spaces, highlighting a distinct stabilization mechanism.

Findings

Optimal paths can stabilize differently in continuous state models.

The stabilization behavior differs fundamentally from finite-state models.

Abstract

This paper deals with convergence of the maximum a posterior probability path estimator in hidden Markov models. We show that when the state space of the hidden process is continuous, the optimal path may stabilize in a way which is essentially different from the previously considered finite-state setting.