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

doi:10.1016/j.aml.2015.04.009

Applied Mathematics Letters

Volume 49, November 2015, Pages 12-19

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Abstract

Explicit formulas for the mean and variance of the solutions of stochastic differential equations with linear drift and diffusion coefficients in state and time 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.

Keywords

Stochastic differential equations

Diffusion process

Local linearization

System identification