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.

Stratonovich integralContinuous-time stochastic processApplied MathematicsMathematical analysisMathematicsofComputing_NUMERICALANALYSISStochastic calculusRiemann–Stieltjes integralRiemann integralsymbols.namesakeQuantum stochastic calculusImproper integralsymbolsDaniell integralAnalysisMathematicsJournal of Mathematical Analysis and Applications
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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.

Thesaurus (information retrieval)Computer scienceSeismic assessment Hysteretic systems Potential systems Moment equations Equivalent non-linearization Stochastic calculus0211 other engineering and technologiesStochastic calculus020101 civil engineering02 engineering and technologyBuilding and Constructionlcsh:TH1-97450201 civil engineeringAlgebraSearch engineSeismic assessmentLinearization021105 building & constructionMoment equationslcsh:Building construction
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