Non-Gaussian models for stochastic mechanics

✍ Scribed by M Grigoriu

• Book ID: 104321267
• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 342 KB
• Volume: 15
• Category: Article
• ISSN: 0266-8920
• DOI: 10.1016/s0266-8920(99)00005-3

✦ Synopsis

Memoryless transformations of Gaussian processes and transformations with memory of the Brownian and Le ´vy processes are used to represent general non-Gaussian processes. The transformations with memory are solutions of stochastic differential equations driven by Gaussian and Le ´vy white noises. The processes obtained by these transformations are referred to as non-Gaussian models. Methods are developed for calibrating these models to records or partial probabilistic characteristics of non-Gaussian processes. The solution of the model calibration problem is not unique. There are different non-Gaussian models that are equivalent in the sense that they are consistent with the available information on a non-Gaussian process. The response analysis of linear and non-linear oscillators subjected to equivalent non-Gaussian models shows that some response statistics are sensitive to the particular equivalent non-Gaussian model used to represent the input. This observation is relevant for applications because the choice of a particular non-Gaussian input model can result in inaccurate predictions of system performance.