Displaying similar documents to “Galerkin-type solution of non-stationary aeroelastic stochastic problems”

Polynomial chaos in evaluating failure probability: A comparative study

Eliška Janouchová, Jan Sýkora, Anna Kučerová (2018)

Applications of Mathematics

Similarity:

Recent developments in the field of stochastic mechanics and particularly regarding the stochastic finite element method allow to model uncertain behaviours for more complex engineering structures. In reliability analysis, polynomial chaos expansion is a useful tool because it helps to avoid thousands of time-consuming finite element model simulations for structures with uncertain parameters. The aim of this paper is to review and compare available techniques for both the construction...

On the convergence of the stochastic Galerkin method for random elliptic partial differential equations

Antje Mugler, Hans-Jörg Starkloff (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Similarity:

In this article we consider elliptic partial differential equations with random coefficients and/or random forcing terms. In the current treatment of such problems by stochastic Galerkin methods it is standard to assume that the random diffusion coefficient is bounded by positive deterministic constants or modeled as lognormal random field. In contrast, we make the significantly weaker assumption that the non-negative random coefficients can be bounded strictly away from zero and infinity...

Symbolic computing in probabilistic and stochastic analysis

Marcin Kamiński (2015)

International Journal of Applied Mathematics and Computer Science

Similarity:

The main aim is to present recent developments in applications of symbolic computing in probabilistic and stochastic analysis, and this is done using the example of the well-known MAPLE system. The key theoretical methods discussed are (i) analytical derivations, (ii) the classical Monte-Carlo simulation approach, (iii) the stochastic perturbation technique, as well as (iv) some semi-analytical approaches. It is demonstrated in particular how to engage the basic symbolic tools implemented...

Modelling Real World Using Stochastic Processes and Filtration

Peter Jaeger (2016)

Formalized Mathematics

Similarity:

First we give an implementation in Mizar [2] basic important definitions of stochastic finance, i.e. filtration ([9], pp. 183 and 185), adapted stochastic process ([9], p. 185) and predictable stochastic process ([6], p. 224). Second we give some concrete formalization and verification to real world examples. In article [8] we started to define random variables for a similar presentation to the book [6]. Here we continue this study. Next we define the stochastic process. For further...

Elliptic equations of higher stochastic order

Sergey V. Lototsky, Boris L. Rozovskii, Xiaoliang Wan (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

This paper discusses analytical and numerical issues related to elliptic equations with random coefficients which are generally nonlinear functions of white noise. Singularity issues are avoided by using the Itô-Skorohod calculus to interpret the interactions between the coefficients and the solution. The solution is constructed by means of the Wiener Chaos (Cameron-Martin) expansions. The existence and uniqueness of the solutions are established under rather weak assumptions, the main...

Tightness of Continuous Stochastic Processes

Michał Kisielewicz (2006)

Discussiones Mathematicae Probability and Statistics

Similarity:

Some sufficient conditins for tightness of continuous stochastic processes is given. It is verified that in the classical tightness sufficient conditions for continuous stochastic processes it is possible to take a continuous nondecreasing stochastic process instead of a deterministic function one.