Theory and Modern Applications
Table 4 Approximation of the expectation of the solution stochastic process. Example 4.1, assuming dependent random data
t | \(\mathbb{E}[X_{15}(t)]\) | \(\mathbb{E}[X_{16}(t)]\) | Dishonest | MC 50,000 | MC 100,000 |
|---|---|---|---|---|---|
0.00 | 1 | 1 | 1 | 1.00287 | 1.00114 |
0.25 | 1.50619 | 1.50619 | 1.49870 | 1.50202 | 1.50134 |
0.50 | 1.98755 | 1.98755 | 1.98750 | 1.99129 | 1.99168 |
0.75 | 2.45120 | 2.45120 | 2.45102 | 2.45529 | 2.45678 |
1.00 | 2.86893 | 2.86893 | 2.86818 | 2.87321 | 2.87583 |
1.25 | 3.23538 | 3.23538 | 3.21339 | 3.22008 | 3.22386 |
1.50 | 3.46485 | 3.46485 | 3.45812 | 3.46878 | 3.47374 |
1.75 | 3.58966 | 3.58966 | 3.57340 | 3.59290 | 3.59902 |
2.00 | 3.56817 | 3.56817 | 3.53286 | 3.57032 | 3.57755 |