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

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.