Ornstein-Uhlenbeck power spectrum

The stationary spectral-density matrix of

d X = - A X d t + b d W

is

S (ω) = (A + iω I)^{- 1} b b^{T} (A^{T} - iω I)^{- 1} .

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Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 353 / 1 / a / ii / Solution

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