Theory and Modern Applications
Table 2 Approximation of the variance of the solution stochastic process. Example 4.1, assuming independent random data
t | \(\mathbb{V}[X_{15}(t)]\) | \(\mathbb{V}[X_{16}(t)]\) | MC 50,000 | MC 100,000 |
|---|---|---|---|---|
0.00 | 1 | 1 | 0.99610 | 0.99530 |
0.25 | 1.06035 | 1.06035 | 1.05902 | 1.05642 |
0.50 | 1.23142 | 1.23142 | 1.23408 | 1.22793 |
0.75 | 1.49261 | 1.49261 | 1.50041 | 1.48944 |
1.00 | 1.81392 | 1.81392 | 1.82744 | 1.81127 |
1.25 | 2.15870 | 2.15870 | 2.17768 | 2.15721 |
1.50 | 2.49379 | 2.49379 | 2.51690 | 2.49462 |
1.75 | 2.80560 | 2.80560 | 2.83029 | 2.81030 |
2.00 | 3.11530 | 3.11530 | 3.13783 | 3.12559 |