Simplified formulas for the mean and variance of linear stochastic differential equations

TL;DR

This paper derives simplified explicit formulas for the mean and variance of linear stochastic differential equations using exponential matrices, improving previous methods and aiding system identification and numerical implementation.

Contribution

It introduces more straightforward formulas for mean and variance calculations, replacing complex higher-dimensional exponential matrix expressions.

Findings

Simplified formulas enhance computational efficiency.

Improved accuracy in system identification.

Facilitates numerical algorithms for stochastic systems.

Abstract

Explicit formulas for the mean and variance of linear stochastic differential equations are derived in terms of an exponential matrix. This result improved a previous one by means of which the mean and variance are expressed in terms of a linear combination of higher dimensional exponential matrices. The important role of the new formulas for the system identification as well as numerical algorithms for their practical implementation are pointed out.