Simplified formulas for the mean and variance of linear stochastic differential equations
Provides a more efficient mathematical tool for researchers and engineers working with linear stochastic differential equations, though the improvement is incremental.
The authors derive explicit formulas for the mean and variance of linear stochastic differential equations using an exponential matrix, improving upon previous methods that required higher-dimensional matrices. The formulas are shown to be useful for system identification and numerical implementation.
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.