Rigorous Computing of Rectangle Scan Probabilities for Markov Increments

TL;DR

This paper presents an algorithm to compute precise bounds for rectangle scan probabilities in Markov increments, enhancing accuracy and understanding of these probabilistic measures.

Contribution

The paper introduces a new algorithm that provides rigorous bounds for rectangle scan probabilities in Markov processes, extending previous work.

Findings

The algorithm computes tight upper and lower bounds.

Experimental results show the bounds are close in practice.

The method's tractability depends on input variable ranges.

Abstract

Extending recent work of Corrado, we derive an algorithm that computes rigorous upper and lower bounds for rectangle scan probabilities for Markov increments. We experimentally examine the closeness of the bounds computed by the algorithm and we examine the range of tractable input variables.