Related papers: Fractional calculus approach to the statistical ch…
Let $X$ be a random variable that takes its values in $\frac{1}{q}\mathbb{Z}$, for some integer $q\ge2$, and consider $X$ rounded to an integer, either downwards or upwards or to the nearest integer. We give general formulas for the…
A unifying and generalizing approach to representations of the positive-part and absolute moments $\mathsf{E} X_+^p$ and $\mathsf{E}|X|^p$ of a random variable $X$ for real $p$ in terms of the characteristic function (c.f.) of $X$, as well…
As high-dimensional and high-frequency data are being collected on a large scale, the development of new statistical models is being pushed forward. Functional data analysis provides the required statistical methods to deal with large-scale…
In this note we introduce the notion of factorial moment distance for non-negative integer-valued random variables and we compare it with the total variation distance. Furthermore, we study the rate of convergence in the classical matching…
Anomalous transport in a tilted periodic potential is investigated numerically within the framework of the fractional Fokker-Planck dynamics via the underlying CTRW. An efficient numerical algorithm is developed which is applicable for an…
This paper defines a new class of fractional differential operators alongside a family of random variables whose density functions solve fractional differential equations equipped with these operators. These equations can be further used to…
A Langevin equation with a special type of additive random source is considered. This random force presents a fractional order derivative of white noise, and leads to a power-law time behavior of the mean square displacement of a particle,…
This paper outlines a unified framework for high dimensional variable selection for classification problems. Traditional approaches to finding interesting variables mostly utilize only partial information through moments (like mean…
In the era of rapidly increasing amounts of time series data, classification of variable objects has become the main objective of time-domain astronomy. Classification of irregularly sampled time series is particularly difficult because the…
Multivariate probability density functions of returns are constructed in order to model the empirical behavior of returns in a financial time series. They describe the well-established deviations from the Gaussian random walk, such as an…
Fractals and multifractals and their associated scaling laws provide a quantification of the complexity of a variety of scale invariant complex systems. Here, we focus on lattice multifractals which exhibit complex exponents associated with…
We review some applications of fractional calculus developed by the author (partly in collaboration with others) to treat some basic problems in continuum and statistical mechanics. The problems in continuum mechanics concern mathematical…
A classical problem of statistical inference is the valid specification of a model that can account for the statistical dependencies between observations when the true structure is dense, intractable, or unknown. To address this problem, a…
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.…
We introduce a new representation of generalized parton distributions and generalized distribution amplitudes that is based on the partial wave decomposition with respect to the complex collinear conformal spin. This decomposition leads us…
Considering the large number of fractional operators that exist, and since it does not seem that their number will stop increasing soon at the time of writing this paper, it is presented for the first time, as far as the authors know, a…
The fluctuation scaling law has universally been observed in a wide variety of phenomena. For counting processes describing the number of events occurred during time intervals, it is expressed as a power function relationship between the…
The number of modes in a probability density function is representative of the complexity of a model and can also be viewed as the number of subpopulations. Despite its relevance, there has been limited research in this area. A novel…
In this paper we consider a fractional stochastic volatility model, that is a model in which the volatility may exhibit a long-range dependent or a rough/antipersistent behavior. We propose a dynamic sequential Monte Carlo methodology that…
The recently proposed fractional scoring scheme is used to attribute publications to percentile rank classes. It is shown that in this way uncertainties and ambiguities in the evaluation of percentile ranks do not occur. Using the…