On the Validity of the Girsanov Transformation Method for Sensitivity Analysis of Stochastic Chemical Reaction Networks

TL;DR

This paper examines the conditions under which the Girsanov Transformation method is valid for sensitivity analysis in stochastic chemical reaction networks, focusing on martingale properties and integrability conditions.

Contribution

It derives exponential integrability conditions ensuring the validity of the Girsanov Transformation method for sensitivity analysis in stochastic chemical networks.

Findings

Exponential integrability conditions guarantee the martingale property.

Conditions are provided in terms of reaction network structure.

Validity depends on commutation of derivatives with expectation.

Abstract

We investigate the validity of the Girsanov Transformation (GT) method for parametric sensitivity analysis of stochastic models of chemical reaction networks. The validity depends on the likelihood ratio process being a martingale and the commutation of a certain derivative with expectation. We derive some exponential integrability conditions which imply both these requirements. We provide further conditions in terms of a reaction network that imply these exponential integrability conditions.