The generalized fuzzy valued θ-Choquet integrals will be established for the given μ-integrable fuzzy valued functions on a general fuzzy measure space, and the convergence theorems of this kind of fuzzy valued integral are being discussed. Furthermore, the whole of integrals is regarded as a fuzzy valued set function on measurable space, the double-null asymptotic additivity and pseudo-double-...

In this paper, we introduce the Choquet-Pettis integral of set-valued mappings and investigate some properties and convergence theorems for the set-valued Choquet-Pettis integrals.

Using fractional calculus we define integrals of the form ∫ b a f(xt)dyt, where x and y are vector-valued Hölder continuous functions of order β ∈ ( 1 3 , 1 2 ) and f is a continuously differentiable function such that f ′ is λ-Höldr continuous for some λ > 1 β − 2. Under some further smooth conditions on f the integral is a continuous functional of x, y, and the tensor product x ⊗ y with respe...

We present an alternative construction of the infinite dimensional Itô integral with respect to a Hilbert space valued Lévy process. This approach is based on the well-known theory of real-valued stochastic integration, and the respective Itô integral is given by a series of Itô integrals with respect to standard Lévy processes. We also prove that this stochastic integral coincides with the Itô...