相关论文: The Characteristic Function of the Cube of a Gauss…
This paper contains an account of arbitrary cubic function fields of characteristic three. We define a standard form for an arbitrary cubic curve and consider its function field. By considering an integral basis for the maximal order of…
We define a characteristic function for probability measures on the signatures of geometric rough paths. We determine sufficient conditions under which a random variable is uniquely determined by its expected signature, thus partially…
An analysis of the characteristic function of Gaussian quadratic forms is presented in [1] to study the performance of multichannel communication systems. This technical report reviews this analysis, obtaining alternative expressions to…
Let $X$ be an arbitrary real-valued random variable (r.v.), with the characteristic function (c.f.) $f$. Integral expressions for the c.f.\ of the r.v.'s $\max(0,X)$ in terms of $f$ are given, as well as other related results. Applications…
We show how Cauchy's Integral Formula and the ideas of Dunford's Holomorphic Functional Calculus (for unbounded operators) can be used to compute the Vacuum Characteristic Function (Quantum Fourier Transform) of quantum random variables…
We calculate a general spectral correlation function of products and ratios of characteristic polynomials for a $N\times N$ random matrix taken from the chiral Gaussian Unitary Ensemble (chGUE). Our derivation is based upon finding an…
We propose in this paper a new method to compute the characteristic function (CF) of generalized Gaussian (GG) random variable in terms of the Fox H function. The CF of the sum of two independent GG random variables is then deduced. Based…
We study L^p properties of Gaussian random series with particular attention to the case of radial functions.
On the basis of the Kac formula of the characteristic function of the random variable defined by values of the quadratic functional $J_T [w]$ on trajectories of the standard Wiener process $\{w\}$, the method of its distribution density is…
The expected value of some complex valued random vectors is computed by means of the indicator function of a designed experiment as known in algebraic statistics. The general theory is set-up and results are obtained for finite discrete…
This manuscript reviews theoretical results and applications related to quadratic forms in Gaussian random variables. It summarizes definitions, canonical representations, exact and approximate distributional results, numerical inversion…
In this work we provide a novel approach for computing the coefficients of the characteristic polynomial of a square matrix. We demonstrate that each coefficient can be efficiently represented by a set of circle graphs. Thus, one can employ…
The master equation of quantum optical density operator is transformed to the equation of characteristic function. The parametric amplification and amplitude damping as well as the phase damping are considered. The solution for the most…
The solvability of the cubic congruence $x^{3}\equiv 2\pmod{p}$ is referred to as the $\textit{cubic character of 2}$. In evaluating the cubic character of 2, we introduce the Eisenstein integers, Gauss and Jacobi sums, and the law of cubic…
We propose an estimator for the mean of random variables in separable real Banach spaces using the empirical characteristic function. Assuming that the covariance operator of the random variable is bounded in a precise sense, we show that…
A characteristic function is a special operator-valued analytic function defined on the open unit ball of $\mathbb{C}^n$ associated with an $n$-tuple of commuting row contraction on some Hilbert space. In this paper, we continue our study…
In this paper, we are concerned with multivariate Gegenbauer approximation of functions defined in the $d$-dimensional hypercube. Two new and sharper bounds for the coefficients of multivariate Gegenbauer expansion of analytic functions are…
In this work, we study probability functions associated with Gaussian mixture models. Our primary focus is on extending the use of spherical radial decomposition for multivariate Gaussian random vectors to the context of Gaussian mixture…
We provide theoretical error bounds for the accurate numerical computation of the quantile function given the characteristic function of a continuous random variable. We show theoretically and empirically that the numerical error of the…
For a graph consisting of parallel connected subgraphs we express the characteristic function of the boundary value problem with generalized Neumann conditions at both joining points via characteristic functions of different boundary…