Pathwise Sensitivity Analysis in Transient Regimes

TL;DR

This paper introduces the instantaneous relative entropy and Fisher information matrix for analyzing the sensitivity of transient stochastic processes, extending existing tools from stationary to non-stationary regimes across various stochastic models.

Contribution

It develops novel sensitivity analysis tools for transient stochastic processes, applicable to Markov chains and stochastic differential equations, with a biological example demonstration.

Findings

Introduces IRE and IFIM for transient regimes

Extends RER and FIM to non-stationary processes

Demonstrates methods on biological reaction network

Abstract

The instantaneous relative entropy (IRE) and the corresponding instanta- neous Fisher information matrix (IFIM) for transient stochastic processes are pre- sented in this paper. These novel tools for sensitivity analysis of stochastic models serve as an extension of the well known relative entropy rate (RER) and the corre- sponding Fisher information matrix (FIM) that apply to stationary processes. Three cases are studied here, discrete-time Markov chains, continuous-time Markov chains and stochastic differential equations. A biological reaction network is presented as a demonstration numerical example.