A reliable Monte Carlo method for the evaluation of first passage times of diffusion processes through boundaries is proposed. A nested algorithm that simulates the first passage time of a suitable tied-down process is introduced to account for undetected crossings that may occur inside each discretization interval of the stochastic differential equation associated to the diffusion. A detailed analysis of the performances of the algorithm is then carried on both via analytical proofs and by means of some numerical examples. The advantages of the new method with respect to a previously proposed numerical-simulative method for the evaluation of first passage times are discussed. Analytical results on the distribution of tied-down diffusion processes are proved in order to provide a theoretical justification of the Monte Carlo method.

A Monte Carlo Method for the Simulation of First Passage Time of Diffusion Processes. / Giraudo M.T.; Sacerdote L.; Zucca C.. - In: METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY. - ISSN 1387-5841. - 3 (2)(2001), pp. 215-231.

A Monte Carlo Method for the Simulation of First Passage Time of Diffusion Processes.

GIRAUDO, Maria Teresa;SACERDOTE, Laura Lea;ZUCCA, CRISTINA
2001

Abstract

A reliable Monte Carlo method for the evaluation of first passage times of diffusion processes through boundaries is proposed. A nested algorithm that simulates the first passage time of a suitable tied-down process is introduced to account for undetected crossings that may occur inside each discretization interval of the stochastic differential equation associated to the diffusion. A detailed analysis of the performances of the algorithm is then carried on both via analytical proofs and by means of some numerical examples. The advantages of the new method with respect to a previously proposed numerical-simulative method for the evaluation of first passage times are discussed. Analytical results on the distribution of tied-down diffusion processes are proved in order to provide a theoretical justification of the Monte Carlo method.
3 (2)
215
231
diffusion processes; tied down processes; first exit time; Monte Carlo methods
Giraudo M.T.; Sacerdote L.; Zucca C.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/60250
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