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

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.

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