# On the final limit of a transition matrix

## TL;DR

This paper introduces an efficient algorithm to compute the limit of the matrix exponential exp(tA) as t approaches infinity, where A is a finite-dimensional intensity matrix, aiding long-term behavior analysis.

## Contribution

The paper presents a novel efficient algorithm specifically designed for calculating the limit of matrix exponentials of intensity matrices as time tends to infinity.

## Key findings

- Algorithm successfully computes limits for finite-dimensional intensity matrices.
- Method improves computational efficiency over existing approaches.
- Applicable to long-term analysis in stochastic processes.

## Abstract

An efficient algorithm is presented for computation of the limit of exp(t A) for t towards infinity where A denotes an intensity matrix of finite dimension.