Theory and Modern Applications
Table 5 Approximation of the variance of the solution stochastic process. Example 4.1, assuming dependent random data
t | \(\mathbb{V}[X_{15}(t)]\) | \(\mathbb{V}[X_{16}(t)]\) | MC 50,000 | MC 100,000 |
|---|---|---|---|---|
0.00 | 1 | 1 | 1.01144 | 1.00603 |
0.25 | 1.31128 | 1.31128 | 1.32213 | 1.31611 |
0.50 | 1.75161 | 1.75161 | 1.73855 | 1.73153 |
0.75 | 2.22370 | 2.22370 | 2.22680 | 2.21842 |
1.00 | 2.72094 | 2.72094 | 2.73668 | 2.72659 |
1.25 | 3.06515 | 3.06515 | 3.20829 | 3.19619 |
1.50 | 3.57031 | 3.57031 | 3.58843 | 3.57424 |
1.75 | 3.83591 | 3.83590 | 3.85507 | 3.83916 |
2.00 | 4.02095 | 4.02100 | 4.04117 | 4.02478 |