# Collective marks and first passage times

## TL;DR

This paper introduces a method using collective marks to derive probability generating functions and moments for first passage times in Markov chains, providing a systematic approach for analyzing these stochastic processes.

## Contribution

It presents a novel method employing collective marks to compute generating functions and moments of first passage times in Markov chains.

## Key findings

- Derived probability generating functions for first passage times.
- Established a system of equations for moments of first passage times.
- Provided a new analytical tool for Markov chain analysis.

## Abstract

Probability generating functions for first passage times of Markov chains are found using the method of collective marks. A system of equations is found which can be used to obtain moments of the first passage times.