A Generalization of a Bin-Based Modification to the Stochastic Simulation Algorithm

TL;DR

This paper extends a bin-based modification to Gillespie's stochastic simulation algorithm, addressing unphysical conditions and ensuring physically realistic results across various initial distributions.

Contribution

It identifies issues with the previous modification and proposes a solution to maintain physical realism during stochastic simulations.

Findings

The modified algorithm reduces storage requirements significantly.

The proposed solution prevents unphysical states during simulations.

The method is applicable to a wide range of initial distributions.

Abstract

In a 1996 paper, See$\beta$elberg, Trautmann and Thorn modified Gillespie's (1975) Monte Carlo algorithm which is used to stochastically simulate the collision and coalescence process. Their modification reduces the storage requirements of the simulation by several orders of magnitude. However, their modification creates unphysical and potentially fatal conditions when used with common initial distributions. We identify those conditions and propose a solution to maintain physically real conditions for all state variables during the evolution of any initial distribution.