Related papers: Functional partial canonical correlation
This paper presents new results on Functional Analysis of Variance for fixed effect models with correlated Hilbert-valued Gaussian error components. The geometry of the Reproducing Kernel Hilbert Space (RKHS) of the error term is considered…
The logarithmic derivative of a point process plays a key role in the general approach, due to the third author, to constructing diffusions preserving a given point process. In this paper we explicitly compute the logarithmic derivative for…
In this study the general formula for differential and integral operations of fractional calculus via fractal operators by the method of cumulative diminution and cumulative growth is obtained. The under lying mechanism in the success of…
We prove that the solution of certain linear stochastic differential equations in Hilbert spaces, namely those with bounded operators as well as the conservative stochastic Schr\"odinger equations, can be obtained - along the lines of the…
Fractional differential calculus is a mathematical tool that has found applications in the study of social and physical behaviors considered ``anomalous''. It is often used when traditional integer derivatives models fail to represent cases…
Because of its ineffectiveness, the usual arithmetic Hilbert-Samuel formula is not applicable in the context of Diophantine Approximation. In order to overcome this difficulty, the present paper presents explicit estimates for arithmetic…
We consider functional linear regression models where functional outcomes are associated with scalar predictors by coefficient functions with shape constraints, such as monotonicity and convexity, that apply to sub-domains of interest. To…
Constructing a classical mechanical system associated with a given quantum mechanical one, entails construction of a classical phase space and a corresponding Hamiltonian function from the available quantum structures and a notion of…
The pair correlation function is a fundamental spatial point process characteristic that, given the intensity function, determines second order moments of the point process. Non-parametric estimation of the pair correlation function is a…
Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this end, we incorporate function-valued reproducing kernel Hilbert…
We present some correlated fractional counting processes on a finite time interval. This will be done by considering a slight generalization of the processes in Borges et al. (2012). The main case concerns a class of space-time fractional…
We consider the sampling problem for functional PCA (fPCA), where the simplest example is the case of taking time samples of the underlying functional components. More generally, we model the sampling operation as a continuous linear map…
Effective Hamiltonians are usually constructed by using canonical transformations or projection techniques. In contrast to this, we present a method for systems with arbitrary Hilbert space based on the introduction of cumulants. Cumulants…
We consider frames F in a given Hilbert space, and we show that every F may be obtained in a constructive way from a reproducing kernel and an orthonormal basis in an ambient Hilbert space. The construction is operator-theoretic, building…
Distance covariance and distance correlation are scalar coefficients that characterize independence of random vectors in arbitrary dimension. Properties, extensions, and applications of distance correlation have been discussed in the recent…
The relationship between discontinuous and continuous stochastic processes in Hilbert space is investigated. It is shown that for any continuos process there is a parent discontinuous process, that becomes the continuous one in the proper…
We investigate varies correlation functions of modular Hamiltonians defined with respect to spatial regions in quantum field theories. These correlation functions are divergent in general. We extract finite correlators by removing divergent…
In the present paper I show how it is possible to derive the Hilbert space formulation of Quantum Mechanics from a comprehensive definition of "physical experiment" and assuming "experimental accessibility and simplicity" as specified by…
We develop a Hungarian construction for the partial sum process of independent non-identically distributed random variables. The process is indexed by functions $f$ from a class $\mathcal{H}$, but the supremum over $f\in $ $\mathcal{H}$ is…
Symmetric Hilbert spaces such as the bosonic and the fermionic Fock spaces over some `one particle space' $\K$ are formed by certain symmetrization procedures performed on the full Fock space. We investigate alternative ways of…