Journal of Probability and Statistics / 2015 / Article / Tab 1

Research Article

On the Computation of the Survival Probability of Brownian Motion with Drift in a Closed Time Interval When the Absorbing Boundary Is a Step Function

Table 1

Numerical comparison between Proposition 1 and conditional Monte Carlo (CMC) approximation1.

Proposition 1CMC
500,000
CMC
5,000,000
CMC
20,000,000

Average divergence (%)00.298740.0214960.00046
Maximum divergence (%)00.842310.138840.087
Computational time (seconds)0.5924.57239.26953.42

The average divergence is the average of the absolute values of the differences between Proposition 1 and CMC divided by Proposition 1 out of a sample of 1,500 lists of randomly drawn parameters.
The maximum divergence is the maximum of the absolute values of the differences between Proposition 1 and CMC divided by Proposition 1 out of a sample of 1,500 lists of randomly drawn parameters.
Computational time is measured on an i3 2.5 Ghz processor.