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Theory and Modern Applications

Table 3 Approximation of \(\mathbb {C}\mathrm {ov}[A(t),\dot{X}(t)]\) and \(\mathbb {C}\mathrm {ov}[B(t),X(t)]\) via accurate truncations \(\dot{X}_{16}(t)\) and \(X_{16}(t)\), respectively. Example 4.1, assuming independent random data

From: Random non-autonomous second order linear differential equations: mean square analytic solutions and their statistical properties

t

\(\mathbb {C}\mathrm {ov}[A(t),\dot{X}_{16}(t)]\)

\(\mathbb {C}\mathrm {ov}[B(t),X_{16}(t)]\)

0.00

0

0

0.25

0

−0.0000325384

0.50

0

−0.000622983

0.75

0

−0.00365252

1.00

0

−0.0130099

1.25

0

−0.0349332

1.50

0

−0.0778424

1.75

0

−0.151444

2.00

0

−0.264968