# Efficient solution of the first passage problem by Path Integration for normal and Poissonian white noise

Mario Di Paola, Christian Bucher, Mario Di Paola

Risultato della ricerca: Article

14 Citazioni (Scopus)

### Abstract

In this paper the first passage problem is examined for linear and nonlinear systems driven by Poissonian and normal white noise input. The problem is handled step-by-step accounting for the Markov properties of the response process and then by Chapman-Kolmogorov equation. The final formulation consists just of a sequence of matrix-vector multiplications giving the reliability density function at any time instant. Comparison with Monte Carlo simulation reveals the excellent accuracy of the proposed method.
Lingua originale English 121-128 8 Probabilistic Engineering Mechanics 41 Published - 2015

### Fingerprint

White noise
white noise
Probability density function
Linear systems
Nonlinear systems
linear systems
nonlinear systems
multiplication
formulations
simulation
Monte Carlo simulation

### All Science Journal Classification (ASJC) codes

• Statistical and Nonlinear Physics
• Civil and Structural Engineering
• Nuclear Energy and Engineering
• Condensed Matter Physics
• Aerospace Engineering
• Ocean Engineering
• Mechanical Engineering

### Cita questo

Efficient solution of the first passage problem by Path Integration for normal and Poissonian white noise. / Di Paola, Mario; Bucher, Christian; Di Paola, Mario.

In: Probabilistic Engineering Mechanics, Vol. 41, 2015, pag. 121-128.

Risultato della ricerca: Article

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AU - Bucher, Christian

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AB - In this paper the first passage problem is examined for linear and nonlinear systems driven by Poissonian and normal white noise input. The problem is handled step-by-step accounting for the Markov properties of the response process and then by Chapman-Kolmogorov equation. The final formulation consists just of a sequence of matrix-vector multiplications giving the reliability density function at any time instant. Comparison with Monte Carlo simulation reveals the excellent accuracy of the proposed method.

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JO - Probabilistic Engineering Mechanics

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