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arxiv: 1207.5067 · v2 · pith:KWGSZGTRnew · submitted 2012-07-20 · 🧮 math.OC · cs.NA· math.NA· math.PR

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

classification 🧮 math.OC cs.NAmath.NAmath.PR
keywords formulaslinearmeanvariancedifferentialequationsexponentialstochastic
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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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