Continuous-Time, Discrete-Event Simulation from Counting Processes

TL;DR

This paper introduces a novel method for continuous-time, discrete-event simulation based on survival analysis and counting processes, enabling accurate modeling of time-dependent intensities with both continuous and atomic components.

Contribution

It provides a structured approach linking survival analysis hazard rates to simulation algorithms, including exact stochastic simulation methods in continuous time.

Findings

Defines a sequence of steps from hazard rates to simulation algorithms

Derives exact stochastic simulation algorithms in continuous time

Handles time-dependent intensities with continuous and atomic components

Abstract

This is a method for discrete event simulation specified by survival analysis. It presents a sequence of steps. First, hazard rates from survival analysis specify the rates of a set of counting processes. Second, those counting processes define a transition kernel. Third, there are four different ways to sample that transition kernel, including a first-principles derivation of exact stochastic simulation algorithms (SSA) in continuous time. This simulation allows time-dependent intensities which include both continuous and atomic components. Separating the steps involved makes a clear correspondence between mathematical formulation and algorithmic implementation.