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Theory and Modern Applications

Table 12 Approximation of the expectation of the solution stochastic process. Example 4.4, assuming independent initial conditions

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

t

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

\(\mathbb{E}[X_{17}(t)]\)

Dishonest

MC 50,000

MC 100,000

0.00

2

2

2

2.01406

1.99858

0.25

2.11267

2.11267

2.11266

2.12676

2.11130

0.50

2.17662

2.17662

2.17654

2.19050

2.17531

0.75

2.15693

2.15693

2.15675

2.17021

2.15573