A Contracted Path Integral Solution of the Discrete Master Equation

TL;DR

This paper introduces a novel contracted path integral approach to solve the discrete master equation, enabling efficient calculation of occurrence time distributions for stochastic processes.

Contribution

It presents a new contracted path integral representation that simplifies solving the discrete master equation and facilitates the development of new computational methods.

Findings

Provides a new exact solution representation for the discrete master equation

Enables calculation of occurrence time probability distributions for each path

Lays groundwork for innovative computational solution techniques

Abstract

A new representation of the exact time dependent solution of the discrete master equation is derived. This representation can be considered as contraction of the path integral solution of Haken. It allows the calculation of the probability distribution of the occurence time for each path and is suitable as basis of new computational solution methods.