A Method to Calculate the Exit Time in Stochastic Simulations

TL;DR

This paper introduces a new method for calculating exit times in stochastic simulations, which improves efficiency by reducing the number of random variates needed while maintaining accuracy.

Contribution

A novel frequency domain approach to approximate exit times in stochastic simulations, enhancing speed and reducing computational cost.

Findings

Achieves faster simulation with fewer random variates.

Provides error analysis and comparison with classical methods.

Demonstrates effective approximation of exit time distributions.

Abstract

A novel method is presented to compute the exit time for the stochastic simulation algorithm. The method is based on the addition of a series of random variables and is derived using the convolution theorem. The final distribution is derived and approximated in the frequency domain. The distribution for the final time is transformed back to the real domain and can be sampled from in a simulation. The result is an approximation of the classical stochastic simulation algorithm that requires fewer random variates. An analysis of the error and speedup compared to the stochastic simulation algorithm is presented.