Representation of Itô integrals by Lebesgue/Bochner integrals

Two Sugeno Integrals Based Representation

The representation of a comonotone-∨̌-additive and monotone functional L, defined on the class of functions from X to [−1, 1], by two Sugeno integrals have been presented. This representation is a generalization of certain previous results, which are useful for the Cumulative Prospect Theory.

Greedy decomposition integrals

In this contribution we define a new class of non-linear integrals based on decomposition integrals. These integrals are motivated by greediness of many real-life situations. Another view on this new class of integrals is that it is a generalization of both the Shilkret and PAN integrals. Moreover, it can be seen as an iterated Shilkret integral. Also, an example in time-series analysis is prov...

Representation of Fourier Integrals as Sums. Iip

provided an = sin (wn/2) and k(x) =sin (irx/2). Weinberger [8] treated the case when the coefficients a„ form a periodic sequence; that is an+q = a„ for some integer q. Making use of the character theory of Dirichlet 7-functions, he found the conditions on the a„ so that (3) holds with the kernel (2/q112) cos (2irx/q) or the kernel (2/q112) sin (2irx/q). (These kernels give self-reciprocal tran...

Local-time representation of path integrals.

We derive a local-time path-integral representation for a generic one-dimensional time-independent system. In particular, we show how to rephrase the matrix elements of the Bloch density matrix as a path integral over x-dependent local-time profiles. The latter quantify the time that the sample paths x(t) in the Feynman path integral spend in the vicinity of an arbitrary point x. Generalization...

On the Representation of Arbitrary Functions by Definite Integrals.