Aim of this paper is an investigation on the consistency of the Path Integration (PI) method already proposed by Naess & Johansen, 1991,1993 for non-linear systems driven by α-stable white noise. It is shown that in the limit, as τ→0, the Einstein-Smoluchowsky (ES) equation is fully restored. Once the consistency of the PI is demonstrated for the half oscillator, then the extension of the ES equation for MDOF system is found starting from the PI method.
Di Paola, M., Iwankiewicz, R., Pirrotta, A. (2009). Non-linear systems under Levy White Noise Handled by path integration method. In Safety, Reliability and Risk of Structures, Infrastructures and Engineering Systems (pp.991-996). London : Furuta, Frangopol & Shinozuka (eds).
Non-linear systems under Levy White Noise Handled by path integration method
DI PAOLA, Mario;PIRROTTA, Antonina
2009-01-01
Abstract
Aim of this paper is an investigation on the consistency of the Path Integration (PI) method already proposed by Naess & Johansen, 1991,1993 for non-linear systems driven by α-stable white noise. It is shown that in the limit, as τ→0, the Einstein-Smoluchowsky (ES) equation is fully restored. Once the consistency of the PI is demonstrated for the half oscillator, then the extension of the ES equation for MDOF system is found starting from the PI method.
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