In the present paper attention will be focus on a special class of one-dimensional Markov processes sharing the features of being both Gauss and diffusion. Contributions in such direction have recently made significant progress as proved for instance in [Lo and Hi, 2006] and [Taillefumier and Magnasco, 2010]. In particular, in [Lo and Hi, 2006] a method is provided for determining the FPT probability mass at any preassigned state value, whereas in [Taillefumier and Magnasco, 2010] a sophisticated, subtle and largely time saving procedure is worked out to simulate the sample paths of the process. Our contribution towards the solution of such problems rests on the following circumstances: the proved existence of an integral equation for the FPT pdf ([Buonocore et al., 1987], [Buonocore et al., 2011], [Di Nardo et al., 2001]), the possibility of evaluating FPT density and distribution function at any given time without need to start afresh the computation as time is changed and the implementation of numerical methods, all this working jointly in an integrated fashion, with consequent significantly increased efficiency and reliability.
First-Passage-Time for Gauss-Diffusion Processes via Integrated Analytical, Simulation and Numerical Methods / Buonocore, Aniello; Caputo, Luigia; Pirozzi, Enrica. - 6927:(2012), pp. 96-104. (Intervento presentato al convegno 13th International Conference EUROCAST 2011 tenutosi a Las Palmas de Gran Canaria, Spain nel 6-11 February 2011) [10.1007/978-3-642-27549-4_13].
First-Passage-Time for Gauss-Diffusion Processes via Integrated Analytical, Simulation and Numerical Methods
BUONOCORE, ANIELLO;CAPUTO, LUIGIA;PIROZZI, ENRICA
2012
Abstract
In the present paper attention will be focus on a special class of one-dimensional Markov processes sharing the features of being both Gauss and diffusion. Contributions in such direction have recently made significant progress as proved for instance in [Lo and Hi, 2006] and [Taillefumier and Magnasco, 2010]. In particular, in [Lo and Hi, 2006] a method is provided for determining the FPT probability mass at any preassigned state value, whereas in [Taillefumier and Magnasco, 2010] a sophisticated, subtle and largely time saving procedure is worked out to simulate the sample paths of the process. Our contribution towards the solution of such problems rests on the following circumstances: the proved existence of an integral equation for the FPT pdf ([Buonocore et al., 1987], [Buonocore et al., 2011], [Di Nardo et al., 2001]), the possibility of evaluating FPT density and distribution function at any given time without need to start afresh the computation as time is changed and the implementation of numerical methods, all this working jointly in an integrated fashion, with consequent significantly increased efficiency and reliability.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
