The Itô-Clifford integral

Integral Representations and its Applications in Clifford Analysis

In this paper, we mainly study the integral representations for functions f with values in a universal Clifford algebra C(Vn,n), where f ∈ Λ(f,Ω), Λ(f,Ω) = { f |f ∈ C∞(Ω, C(Vn,n)),max x∈Ω ∣∣Djf(x)∣∣ = = O(M )(j → +∞), for someM, 0 < M < +∞} . The integral representations of Tif are also given. Some properties of Tif and Πf are shown. As applications of the higher order Pompeiu formula, we get t...

An integral sliding mode control approach to observer-based stabilization of stochastic Itô descriptor systems

This paper is concerned with sliding mode observer design and observer-based sliding mode controller synthesis for stochastic Itô descriptor systems. A novel integral sliding surface, which involves a product of sliding variable and a negative definite matrix, is constructed for the error system. It is shown that the product term not only has a stabilizing effect on the sliding variable, but al...

Haar Wavelets Approach For Solving Multidimensional Stochastic Itô - Volterra Integral Equations ∗

A new computational method based on Haar wavelets is proposed for solving multidimensional stochastic Itô-Volterra integral equations. The block pulse functions and their relations to Haar wavelets are employed to derive a general procedure for forming stochastic operational matrix of Haar wavelets. Then, Haar wavelets basis along with their stochastic operational matrix are used to approximate...

A numerical method for solving m-dimensional stochastic Itô-Volterra integral equations by stochastic operational matrix

Clifford Wavelets and Clifford-valued MRAs

In this paper using the Clifford algebra over R4 and its matrix representation, we construct Clifford scaling functions and Clifford wavelets. Then we compute related mask functions and filters, which arise in many applications such as quantum mechanics.