Fuzzy Stochastic Differential Equations Driven by Semimartingales-Different Approaches – ScienceOpen
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      Fuzzy Stochastic Differential Equations Driven by Semimartingales-Different Approaches

      Mathematical Problems in Engineering
      Hindawi Limited

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          Abstract

          The first aim of the paper is to present a survey of possible approaches for the study of fuzzy stochastic differential or integral equations. They are stochastic counterparts of classical approaches known from the theory of deterministic fuzzy differential equations. For our aims we present first a notion of fuzzy stochastic integral with a semimartingale integrator and its main properties. Next we focus on different approaches for fuzzy stochastic differential equations. We present the existence of fuzzy solutions to such equations as well as their main properties. In the first approach we treat the fuzzy equation as an abstract relation in the metric space of fuzzy sets over the space of square integrable random vectors. In the second one the equation is interpreted as a system of stochastic inclusions. Finally, in the last section we discuss fuzzy stochastic integral equations with solutions being fuzzy stochastic processes. In this case the notion of the stochastic Itô’s integral in the equation is crisp; that is, it has single-valued level sets. The second aim of this paper is to show that there is no extension to more general diffusion terms.

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          Fuzzy differential equations

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            Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations

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              Differentials of fuzzy functions

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                Author and article information

                Journal
                Mathematical Problems in Engineering
                Mathematical Problems in Engineering
                Hindawi Limited
                1024-123X
                1563-5147
                2015
                2015
                : 2015
                :
                : 1-9
                Article
                10.1155/2015/794607
                aceaf3b9-1610-410a-9d8d-340c45ce0ff2
                © 2015

                http://creativecommons.org/licenses/by/3.0/

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