Set-Valued Stochastic Integrals with Respect to Finite Variation Processes
نویسندگان
چکیده
In a Euclidean space , the Lebesgue-Stieltjes integral of set-valued stochastic processes d R , 0, t F F t T with respect to real valued finite variation process , 0, t A t T t is defined directly by employing all integrably bounded selections instead of taking the decomposable closure appearing in some existed references. We shall show that this kind of integral is measurable, continuous in under the Hausdorff metric and -bounded. 2 L
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Probability theory is an important tool of modeling randomness in a practical problem. But besides randomness, in the real world, there exists other kind of uncertainties such as impreciseness or vagueness. Set-valued functions are employed to model the impreciseness in applied field such as in Economics, control theory (see for example [1]). Integrals of set-valued functions have been received...
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