On Equations with a Fuzzy Stochastic Integral with Respect to Semimartingales

Abstract

We consider some equations in a metric space of fuzzy sets with basis of square integrable random vectors. These equations generalize the single-valued stochastic differential equations and set-valued stochastic integral equations as well. A main object is a fuzzy stochastic trajectory integral with respect to a semimartingale. We obtain the existence and uniqueness of global solutions to fuzzy stochastic integral equations driven by continuous semimartingales. Also, we present a stability of solutions under changes of equation’s data.KeywordsFuzzy stochastic integralfuzzy stochastic integral equation