Search results for " Stochastic calculus"
showing 2 items of 12 documents
Set-valued stochastic integral equations driven by martingales
2012
Abstract We consider a notion of set-valued stochastic Lebesgue–Stieltjes trajectory integral and a notion of set-valued stochastic trajectory integral with respect to martingale. Then we use these integrals in a formulation of set-valued stochastic integral equations. The existence and uniqueness of the solution to such the equations is proven. As a generalization of set-valued case results we consider the fuzzy stochastic trajectory integrals and investigate the fuzzy stochastic integral equations driven by bounded variation processes and martingales.
Equivalent Non-Linearization of Hysteretic Systems by Means of RPS
2018
BackgroundThe analysis of elastoplastic systems with hardening (Bouc-Wen systems) under stochastic (seismic) loads needs the evaluation of higher order statistics even in the simplest case of normal distributed input. ObjectiveIn this paper, a non-linearization technique is proposed in order to evaluate the moments of any order of the response. MethodThis technique is developed by means of a nonlinear class of systems whose statistics are a priori known. The parameters of such systems can be chosen in such a way that the two systems are equivalent in a wide sense. Result & ConclusionIn the paper, the strategy to obtain the equivalence and the reliability of the results are discussed.