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Theory and Modern Applications

Table 14 Approximation of the expectation of the solution stochastic process. Example 4.4, assuming dependent initial conditions

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

t

\(\mathbb{E}[X_{15}(t)]\)

\(\mathbb{E}[X_{16}(t)]\)

Dishonest

MC 50,000

MC 100,000

0.00

0.87

0.87

0.87

0.866780

0.869210

0.25

0.973828

0.973828

0.973819

0.970205

0.973499

0.50

1.04817

1.04817

1.0481

1.04427

1.04823

0.75

1.07358

1.07358

1.0734

1.06961

1.07394