Related papers: Distribution Functions for Random Variables for En…
It has been observed that the statistical distribution of the eigenvalues of random matrices possesses universal properties, independent of the probability law of the stochastic matrix. In this article we find the correlation functions of…
Asymptotic expansion is presented for an estimator of the Hurst coefficient of a fractional Brownian motion. For this, a recently developed theory of asymptotic expansion of the distribution of Wiener functionals is applied. The effects of…
We consider large non-Hermitian random matrices $X$ with complex, independent, identically distributed centred entries and show that the linear statistics of their eigenvalues are asymptotically Gaussian for test functions having…
The full width at half maximum (FWHM) is a useful quantity for characterizing the bandwidth of unimodal functions. However, a closed-form expression for the FWHM of gamma-shaped functions-i.e. functions that are shaped like the gamma…
We study limit distributions of independent random matrices as well as limit joint distributions of their blocks under normalized partial traces composed with classical expectation. In particular, we are concerned with the ensemble of…
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…
We develop the basic building blocks of a frequency domain framework for drawing statistical inferences on the second-order structure of a stationary sequence of functional data. The key element in such a context is the spectral density…
We develop an analytic theory of operator-valued additive free convolution in terms of subordination functions. In contrast to earlier investigations our functions are not just given by power series expansions, but are defined as Frechet…
We find a formula that relates the Fourier transform of a radial function on $\mathbf{R}^n$ with the Fourier transform of the same function defined on $\mathbf{R}^{n+2}$. This formula enables one to explicitly calculate the Fourier…
In the present work we show that the joint probability distribution of the eigenvalues can be expressed in terms of a differential operator acting on the distribution of some other matrix quantities. Those quantities might be the diagonal…
Let $\xi_0,\xi_1,\ldots$ be independent identically distributed complex- valued random variables such that $\mathbb{E}\log(1+|\xi _0|)<\infty$. We consider random analytic functions of the form…
Let X,Y,B be three independent random variables such that $X$ has the same distribution function as Y B. Assume that B is a Beta random variable with positive parameters a,b and Y has distribution function H. Pakes and Navarro (2007) show…
Using a recently derived integral in terms of elementary functions, we derive new asymptotic expansions of the normal inverse Gaussian cumulative distribution function. One of the asymptotic representations is in terms of the normal…
We rewrite Arthur's asymptotic formula for weighted orbital integrals on real groups with the aid of a residue calculus and extend the resulting formula to the Schwartz space. Then we extract the available information about the coefficients…
Exact formulas are derived for the probability density functions of the sum and difference of two independent non-central gamma distributed random variables, with both series and integral representations of the density presented. These…
We obtain exact formulas for the cumulative distribution function of the variance-gamma distribution, as infinite series involving the modified Bessel function of the second kind and the modified Lommel function of the first kind. From…
We consider the smallest eigenvalue distributions of some Freud unitary ensembles, that is, the probabilities that all the eigenvalues of the Hermitian matrices from the ensembles lie in the interval $(t,\infty)$. This problem is related to…
We provide sharp estimates for the distribution function of a martingale transform of the indicator function of an event. They are formulated in terms of Burkholder functions, which are reduced to the already known Bellman functions for…
The explicit expression for the the probability distribution function of the endpoint fluctuations of one-dimensional directed polymers in random potential is derived in terms of the Bethe ansatz replica technique by mapping the replicated…
Application of the exact statistical inference frequently leads to a non-standard probability distributions of the considered estimators or test statistics. The exact distributions of many estimators and test statistics can be specified by…