FIRST-PASSAGE-TIME PROBLEM FOR SIMULATED STOCHASTIC DIFFUSION-PROCESSES

Solving the first-passage-time problem for one-dimensional stochastic diffusion processes is a task with many applications in biomedical research. It has been noted (Musila and Lansky, Int. J. Biomed. Comput. 31, 233-245, 1992) that the first-passage time is overestimated if computed as the time when the simulated trajectory of the process crosses the threshold. It is studied in this paper how the error depends on the simulation step and on the parameters of the process. We propose an adaptive algorithm to make the simulation faster. The presented examples are related to neuronal modelling, but application in other fields is straightforward.