Theory and Modern Applications
Table 7 Approximation of the expectation of the solution stochastic process. Example 4.2
t | \(\mathbb{E}[X_{15}(t)]\) | \(\mathbb{E}[X_{16}(t)]\) | Dishonest | MC 50,000 | MC 100,000 |
|---|---|---|---|---|---|
0.00 | 1 | 1 | 1 | 0.99750 | 0.99919 |
0.25 | 1.32907 | 1.32907 | 1.32889 | 1.32619 | 1.32703 |
0.50 | 1.26473 | 1.26473 | 1.26175 | 1.26351 | 1.26219 |
0.75 | 0.74510 | 0.74510 | 0.72906 | 0.74737 | 0.74316 |
1.00 | −0.27157 | −0.27157 | −0.32467 | −0.26484 | −0.27144 |
1.25 | −1.80636 | −1.80635 | −1.93991 | −1.79597 | −1.80237 |
1.50 | −3.85882 | −3.85868 | −4.13681 | −3.84872 | −3.84906 |
1.75 | −6.40911 | −6.40754 | −6.90081 | −6.40873 | −6.39186 |
2.00 | −9.43553 | −9.42222 | −10.1448 | −9.46498 | −9.41066 |