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Theory and Modern Applications

Table 8 Approximation of the variance of the solution stochastic process. Example 4.2

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

t

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

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

MC 50,000

MC 100,000

0.00

1

1

0.98671

1.00327

0.25

0.77433

0.77433

0.76716

0.77821

0.50

0.37752

0.37752

0.37822

0.37992

0.75

0.54181

0.54181

0.53554

0.54357

1.00

2.10396

2.10396

2.06444

2.10993

1.25

5.48674

5.48670

5.40047

5.50378

1.50

10.4476

10.4467

10.3456

10.4828

1.75

18.0186

18.0108

17.9539

18.0963

2.00

43.5731

43.6462

43.5773

44.1340