P. Lansky et V. Lanska, FIRST-PASSAGE-TIME PROBLEM FOR SIMULATED STOCHASTIC DIFFUSION-PROCESSES, Computers in biology and medicine, 24(2), 1994, pp. 91-101
Solving the first-passage-time problem for one-dimensional stochastic
diffusion processes is a task with many applications in biomedical res
earch. It has been noted (Musila and Lansky, Int. J. Biomed. Comput. 3
1, 233-245, 1992) that the first-passage time is overestimated if comp
uted as the time when the simulated trajectory of the process crosses
the threshold. It is studied in this paper how the error depends on th
e simulation step and on the parameters of the process. We propose an
adaptive algorithm to make the simulation faster. The presented exampl
es are related to neuronal modelling, but application in other fields
is straightforward.