Related papers: Using fractional derivatives to derive marginal de…
We introduce a novel method for obtaining a wide variety of moments of any random variable with a well-defined moment-generating function (MGF). We derive new expressions for fractional moments and fractional absolute moments, both central…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
In the present article, a new method for the evaluation of fractional derivatives of arbitrary real order is proposed. Numerous but inequivalent formulations have been given in the past. Some of them exhibit unsatisfactory properties such…
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…
We outline an efficient method for the reconstruction of a probability density function from the knowledge of its infinite sequence of ordinary moments. The approximate density is obtained resorting to maximum entropy technique, under the…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
In this article, we consider fractional derivatives of local time for $d-$dimensional centered Gaussian processes satisfying certain strong local nondeterminism property. We first give a condition for existence of fractional derivatives of…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
We propose a new approach for deriving probabilistic inequalities based on bounding likelihood ratios. We demonstrate that this approach is more general and powerful than the classical method frequently used for deriving concentration…
We derive and apply a partial differential equation for the moment generating function of the Wright-Fisher model of population genetics.
Gradient-based techniques are becoming increasingly critical in quantitative fields, notably in statistics and computer science. The utility of these techniques, however, ultimately depends on how efficiently we can evaluate the derivatives…
The concept of moment differentiation is extended to the class of moment summable functions, giving rise to moment differential properties. The main result leans on accurate upper estimates for the integral representation of the moment…
High-dimensional probability density estimation for inference suffers from the "curse of dimensionality". For many physical inference problems, the full posterior distribution is unwieldy and seldom used in practice. Instead, we propose…
Fractional moments have been investigated by many authors to represent the density of univariate and bivariate random variables in different contexts. Fractional moments are indeed important when the density of the random variable has…
The density hypothesis on random times becomes now a standard in modeling of risks. One of the basic reasons to introduce the density hypothesis is the desire to have a computable credit risk model. However, recent work shows that merely an…
A new formalism is presented for finding equilibrium distribution functions for axisymmetric systems. The formalism, obtainded by using the concept of fractional derivatives, generalizes the methods of Fricke (1952), Kalnajs (1972) and…
We develop a general approach to estimating the derivative of a function-valued parameter $\theta_o(u)$ that is identified for every value of $u$ as the solution to a moment condition. This setup in particular covers many interesting models…
Atomic partial charges are crucial parameters for Molecular Dynamics (MD) simulations, molecular mechanics calculations, and virtual screening, as they determine the electrostatic contributions to interaction energies. Current methods for…
We consider the problem of conditional density estimation, which is a major topic of interest in the fields of statistical and machine learning. Our method, called Marginal Contrastive Discrimination, MCD, reformulates the conditional…
Existing deterministic variational inference approaches for diffusion processes use simple proposals and target the marginal density of the posterior. We construct the variational process as a controlled version of the prior process and…