Skip to main content

Theory and Modern Applications

Table 9 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 4.2

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

−0.0345004

0.50

0

−0.145742

0.75

0

−0.322733

1.00

0

−0.515142

1.25

0

−0.612961

1.50

0

−0.403919

1.75

0

0.522644

2.00

0

3.0078