6533b7dcfe1ef96bd1271f9d

RESEARCH PRODUCT

First-passage problem for nonlinear systems under Lévy white noise through path integral method

Antonina PirrottaAntonina PirrottaMario Di PaolaAlberto Di MatteoChristian Bucher

subject

Mathematical optimizationPath integralMonte Carlo methodAerospace Engineering020101 civil engineeringOcean EngineeringProbability density function02 engineering and technologyLévy white noise0201 civil engineering0203 mechanical engineeringApplied mathematicsElectrical and Electronic EngineeringMathematicsFirst passageApplied MathematicsMechanical EngineeringWhite noiseFunction (mathematics)Nonlinear systemAlpha (programming language)020303 mechanical engineering & transportsControl and Systems EngineeringPath integral formulationNonlinear systemRandom variable

description

In this paper, the first-passage problem for nonlinear systems driven by $$\alpha $$ -stable Levy white noises is considered. The path integral solution (PIS) is adopted for determining the reliability function and first-passage time probability density function of nonlinear oscillators. Specifically, based on the properties of $$\alpha $$ -stable random variables and processes, PIS is extended to deal with Levy white noises with any value of the stability index $$\alpha $$ . Application to linear and nonlinear systems considering different values of $$\alpha $$ is reported. Comparisons with pertinent Monte Carlo simulation data demonstrate the accuracy of the results.

yearjournalcountryeditionlanguage
2016-04-07
10.1007/s11071-016-2770-9http://hdl.handle.net/10447/193545