The first-crossing-time p.d.f. evaluation for non-Markov processes is approached by simulating the sample paths of normal processes possessing preassigned spectral densities of a rational type. The simulation algorithm is based on a method due to Franklin (1965), suitably vectorized. The first-crossing-time p.d.f. for various types of boundaries is thus directly estimated by inspection of the simulated sample paths. Our simulations deal with two different types of covariance functions characterized by one and by two parameters, respectively. On the grounds of the results thus far obtained asymptotic esponential trends for large boundaries appear to be exhibited by the first-crossing-time densities, in analogy with the case of Markov diffusion processes. Some other interesting features of these densities are also pointed out.
Simulation of normal processes for first-crossing densities evaluations
DI CRESCENZO, Antonio;
1990-01-01
Abstract
The first-crossing-time p.d.f. evaluation for non-Markov processes is approached by simulating the sample paths of normal processes possessing preassigned spectral densities of a rational type. The simulation algorithm is based on a method due to Franklin (1965), suitably vectorized. The first-crossing-time p.d.f. for various types of boundaries is thus directly estimated by inspection of the simulated sample paths. Our simulations deal with two different types of covariance functions characterized by one and by two parameters, respectively. On the grounds of the results thus far obtained asymptotic esponential trends for large boundaries appear to be exhibited by the first-crossing-time densities, in analogy with the case of Markov diffusion processes. Some other interesting features of these densities are also pointed out.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
