An improved technique for the simulation of first passage times for diffusion processes

Abstract

Improved simulation schemes for the evaluation of first passage times through boundaries for one dimensional diffusion processes can be obtained taking into account possible crossings that occur inside each simulation interval. Approximated evaluations for the probabilities of such events are proposed and the error connected with their use in a simulation algorithm is discussed. Two examples are finally given to illustrate the features of the method.

Keywords:

• tied-down processes
• exit time
• time dependent boundaries
• Feller process
• Ornstein-Uhlenbeck process