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Fractional generalizations of the Poisson process and branching Furry process are considered. The link between characteristics of the processes, fractional differential equations and Levy stable densities are discussed and used for…
We discuss the predictions of chiral quark models for basic pion properties entering high-energy processes: generalized parton distributions (GPD's) and unintegrated parton distributions (UPD's). We stress the role of the QCD evolution,…
An important issue in survival analysis is the investigation and the modeling of hazard rates. Within a Bayesian nonparametric framework, a natural and popular approach is to model hazard rates as kernel mixtures with respect to a…
Within the study of uncertain dynamical systems, iterated random functions are a key tool. There, one samples a family of functions according to a stationary distribution. Here, we introduce an extension, where one sample functions…
Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…
We propose threshold diffusion processes as unique solutions to stochastic differential equations with step-function coefficients, and obtain explicit expressions for the conditional Laplace transform of the hitting times and the potential…
After collecting data from observations or experiments, the next step is to build an appropriate mathematical or stochastic model to describe the data so that further studies can be done with the help of the models. In this article, the…
This paper introduces and studies a new class of nonparametric prior distributions. Random probability distribution functions are constructed via normalization of random measures driven by increasing additive processes. In particular, we…
The study of systems with memory requires methods which are different from the methods used in regular dynamics. Systems with power-law memory in many cases can be described by fractional differential equations, which are…
The modeling and analysis of lifetimes is an important aspect of statistical work in a wide variety of scientific and technological fields. For the first time, the called Kumaraswamy Pareto distribution is introduced and studied. The new…
Identifying upstream processes responsible for wafer defects is challenging due to the combinatorial nature of process flows and the inherent variability in processing routes, which arises from factors such as rework operations and random…
Assuming some regression model, it is common to study the conditional distribution of survival given covariates. Here, we consider the impact of further conditioning, specifically conditioning on a marginal survival function, known or…
We give a brief overview on the theory and phenomenology of generalized parton distributions (GPDs), including the recently developed framework of single-diffractive hard exclusive process for matching GPDs to experimental observables. We…
A new family of fractional counting processes based on a three-parameter generalized Mittag-Leffler function was introduced and studied. As applications we develop a fractional generalized compound process, introduce and develop fractional…
We derive new approximations for the Value at Risk and the Expected Shortfall at high levels of loss distributions with positive skewness and excess kurtosis, and we describe their precisions for notable ones such as for exponential, Pareto…
In this paper we introduce and study three classes of fractional periodic processes. An application to ring polymers is investigated. We obtain a closed analytic expressions for the form factors, the Debye functions and their asymptotic…
We continue to develop a new approach to description of charge kinetics in disordered semiconductors. It is based on fractional diffusion equations. This article is devoted to transient processes in structures under dispersive transport…
This paper introduces a new stochastic process with values in the set Z of integers with sign. The increments of process are Poisson differences and the dynamics has an autoregressive structure. We study the properties of the process and…
We first describe a general class of optimization problems that describe many natural, economic, and statistical phenomena. After noting the existence of a conserved quantity in a transformed coordinate system, we outline several instances…
In clinical trials involving both mortality and morbidity, an active treatment can influence the observed risk of the first non-fatal event either directly, through its effect on the underlying non-fatal event process, or indirectly,…