Computer-aided simulations of Gaussian processes and related asymptotic properties

A parallel algorithm is implemented to simulate sample paths of stationary normal processes possessing a Butterworth-type covariance, in order to investigate asymptotic properties of the first passage time probability densities for time-varying boundaries. After a self-contained outline of the simulation procedure, computational results are included to show that for large times and for large boundaries the first passage time probability density through an asymptotically periodic boundary is exponentially distributed to an excellent degree of approximation

Computer-aided simulations of Gaussian processes and related asymptotic properties

A parallel algorithm is implemented to simulate sample paths of stationary normal processes possessing a Butterworth-type covariance, in order to investigate asymptotic properties of the first passage time probability densities for time-varying boundaries. After a self-contained outline of the simulation procedure, computational results are included to show that for large times and for large boundaries the first passage time probability density through an asymptotically periodic boundary is exponentially distributed to an excellent degree of approximation

Computer-aided simulations of Gaussian processes and related asymptotic properties (Extended Abstract)

It has often been pointed out that first-passage-time (FPT) probability density functions (pdf's) through generally time-dependent boundaries play an essential role for the stochastic description of the behavior of various biological systems. The present paper is the natural extension of some investigations carried out for the class of one-dimensional diffusion processes admitting steady state densities in the presence of single asymptotically constant boundaries or of single asymptotically periodic boundarie