| Mean (Monte Carlo Simulation) | Mean (Theory Equation (20)) | Std. Dev. (Monte Carlo Simulation) | Std. Dev. (Theory Equation (23)) |
t = 10 |
|
|
|
|
x | −0.0123 |
| 3.2095 |
|
y | −0.0080 |
| 3.2205 |
|
z | 0.0389 |
| 3.2338 |
|
Average | 0.0062 | 0.0 | 3.2213 | 3.0848 |
r | 5.0802 | 4.8830 | 2.3070 | 2.1692 |
t = 50 |
|
|
|
|
x | −0.0345 |
| 6.2989 |
|
y | −0.0209 |
| 6.3027 |
|
z | 0.0225 |
| 6.3196 |
|
Average | −0.0110 | 0.0 | 6.3071 | 6.2727 |
r | 9.6762 | 9.6547 | 5.0705 | 4.9828 |
t = 100 |
|
|
|
|
x | 0.0215 |
| 7.9626 |
|
y | 0.0259 |
| 7.9500 |
|
z | −0.0037 |
| 7.9225 |
|
Average | 0.0146 | 0.0 | 7.9450 | 7.9506 |
r | 11.8653 | 11.9176 | 6.9704 | 6.8998 |
t = 1000 |
|
|
|
|
x | 0.0122 |
| 9.9410 |
|
y | −0.0252 |
| 9.9394 |
|
z | −0.0035 |
| 9.9085 |
|
Average | −0.0055 | 0.0 | 9.9296 | 9.9998 |
r | 14.0043 | 14.1421 | 9.9835 | 9.9995 |