Set-Valued Stochastic Integrals with Respect to Finite Variation Processes

Set-Valued Stochastic Integrals with Respect to Finite Variation Processes

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 integr...

Lebesgues-Stieltjes Integrals of Fuzzy Stochastic Processes with Respect to Finite Variation Processes

Let ( ) [ ] { } t G G t T = ∈ ω , 0, be a fuzzy stochastic process and ( ) [ ] { } t A t T ∈ ω , 0, be a real valued finite variation process. We define the Lebesgue-Stieltjes integral denoted by ( ) ( ) ∫ t s s G A ω ω 0 d for each t > 0 by using the selection method, which is direct, nature and different from the indirect definition appearing in some references. We shall show that this kind o...

INTEGRABILITY OF AN INTERVAL-VALUED MULTIFUNCTION WITH RESPECT TO AN INTERVAL-VALUED SET MULTIFUNCTION

Intervals are related to the representation of uncertainty. In this sense, we introduce an integral of Gould type for an interval-valued multifunction relative to an interval-valued set multifunction, with respect to Guo and Zhang order relation. Classicaland specific properties of this new type of integral are established and several examples and applications from multicriteria decision making...

Some Results on Set-valued Stochastic Integrals with Respect to Poisson Jump in an M-type 2 Banach Space

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...

A Probability Bound for Integrals with Respect to Stochastic Processes with Independent Increments1