We develop a stochastic calculus that makes it easy to capture variety of predictable transformations semimartingales such as changes variables, integrals, and their compositions. The framework offers unified treatment real-valued complex-valued semimartingales. proposed is blueprint for the derivation new relationships among processes with specific examples provided below.

We introduce the notion of scalar fuzzy McShane and Henstock integrals for number valued functions we discuss their relationship give a version Gordon theorem [24].

We present moment inequalities for completely degenerate Banach space valued (generalized) U-statistics of arbitrary order. The estimates involve suprema of empirical processes, which in the real valued case can be replaced by simpler norms of the kernel matrix (i.e. norms of some multilinear operators associated with the kernel matrix). As a corollary we derive tail inequalities for U-statisti...

Sugeno integrals are a well-known family of qualitative multiple criteria aggregation operators. The paper investigates how the behavior of these operators can be described in a prioritized propositional logic language, namely possibilistic logic. The case of binary-valued criteria, which amounts to providing a logical description of the fuzzy measure underlying the integral, is first considere...

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...

In this paper we give a simple proof of inequalities of integrals of functions which are the composition of nonnegative continous convex functions on a vector space R and vector-valued functions in a weakly compact subset of a Banach vector space generated by m Lμ-spaces for 1 ≤ p < +∞. Also, the same inequalities hold if these vector-valued functions are in a weakly* compact subset of a Banach...