A closed form approximation and error quantification for the response transition probability density function of a class of stochastic differential equations. (October 2018)

• Record Type: Journal Article
• Authors: Meimaris, Antonios T.; Kougioumtzoglou, Ioannis A.; Pantelous, Athanasios A.
• Is Part Of: Probabilistic engineering mechanics. Volume 54(2018)
• Page Start: 87
• Page End: 94
• Publication Date: 2018-10
• Subjects: Stochastic differential equations -- Stochastic dynamics -- Path integral -- Error quantification -- Cauchy–Schwarz inequality; Engineering -- Statistical methods -- Periodicals; Mechanics, Applied -- Statistical methods -- Periodicals; Probabilities -- Periodicals; Ingénierie -- Méthodes statistiques -- Périodiques; Mécanique appliquée -- Méthodes statistiques -- Périodiques; Probabilités -- Périodiques; 620.100727
• DOI: 10.1016/j.probengmech.2017.07.005
• Languages: English
• ISSNs: 0266-8920

Abstract

Abstract: A closed-form analytical approximation is derived for the response transition probability density function (PDF) of a certain class of stochastic differential equations with constant drift and nonlinear diffusion coefficients. This is done by resorting to a recently developed Wiener path integral based technique (WPI) in conjunction with a Cauchy–Schwarz inequality treatment of the problem. The derived approximation can be used, due to its analytical nature, as a direct SDE response PDF estimate that requires zero computational effort for its determination. Further, it facilitates an error quantification analysis, which yields an a priori estimate of the anticipated accuracy obtained by applying the approximate methodology. The reliability of the approximation is demonstrated via several engineering mechanics/dynamics related numerical examples pertaining to the stochastic beam bending problem, as well as to the response determination of stochastically excited nonlinear oscillators.