Theory and Modern Applications
Table 1 Approximation of the expectation of the solution stochastic process. Example 4.1, assuming independent 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 | 0.99701 | 1.00138 |
0.25 | 1.49870 | 1.49870 | 1.49870 | 1.49519 | 1.49976 |
0.50 | 1.98752 | 1.98752 | 1.98752 | 1.98353 | 1.98829 |
0.75 | 2.45108 | 2.45108 | 2.45102 | 2.44667 | 2.45160 |
1.00 | 2.86856 | 2.86856 | 2.86818 | 2.86383 | 2.86893 |
1.25 | 3.21494 | 3.21494 | 3.21339 | 3.21008 | 3.21534 |
1.50 | 3.46310 | 3.46310 | 3.45812 | 3.45831 | 3.46376 |
1.75 | 3.58660 | 3.58660 | 3.57340 | 3.58215 | 3.58784 |
2.00 | 3.56336 | 3.56335 | 3.53286 | 3.55948 | 3.56552 |