TY - CHAP

T1 - Complex fractional moments for the characterization of the probabilistic response of non-linear systems subjected to white noises

AU - Di Paola, Mario

AU - Pirrotta, Antonina

AU - Pinnola, Francesco Paolo

AU - Di Matteo, Alberto

AU - Alotta, Gioacchino

AU - Pinnola, Francesco Paolo

PY - 2019

Y1 - 2019

N2 - In this chapter the solution of Fokker-Planck-Kolmogorov type equations is pursued with the aid of Complex Fractional Moments (CFMs). These quantities are the generalization of the well-known integer-order moments and are obtained as Mellin transform of the Probability Density Function (PDF). From this point of view, the PDF can be seen as inverse Mellin transform of the CFMs, and it can be obtained through a limited number of CFMs. These CFMs’ capability allows to solve the Fokker-Planck-Kolmogorov equation governing the evolutionary PDF of non-linear systems forced by white noise with an elegant and efficient strategy. The main difference between this new approach and the other one based on integer moments lies in the fact that CFMs do not require the closure scheme because a limited number of them is sufficient to accurately describe the evolutionary PDF and no hierarchy problem occurs.

AB - In this chapter the solution of Fokker-Planck-Kolmogorov type equations is pursued with the aid of Complex Fractional Moments (CFMs). These quantities are the generalization of the well-known integer-order moments and are obtained as Mellin transform of the Probability Density Function (PDF). From this point of view, the PDF can be seen as inverse Mellin transform of the CFMs, and it can be obtained through a limited number of CFMs. These CFMs’ capability allows to solve the Fokker-Planck-Kolmogorov equation governing the evolutionary PDF of non-linear systems forced by white noise with an elegant and efficient strategy. The main difference between this new approach and the other one based on integer moments lies in the fact that CFMs do not require the closure scheme because a limited number of them is sufficient to accurately describe the evolutionary PDF and no hierarchy problem occurs.

KW - Complex fractional moments

KW - Fokker-Planck equation

KW - Probability density function

KW - Complex fractional moments

KW - Fokker-Planck equation

KW - Probability density function

UR - http://hdl.handle.net/10447/391649

UR - http://www.springer.com/series/361

M3 - Chapter

SN - 978-981-13-9462-1; 978-981-13-9463-8

T3 - SPRINGER PROCEEDINGS IN PHYSICS

SP - 203

EP - 227

BT - Topics in Nonlinear Mechanics and Physics, Selected papers from CSNDD 2018

ER -