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An intermittent nonlinear map generating subdiffusion is investigated. Computer simulations show that the generalized diffusion coefficient of this map has a fractal, discontinuous dependence on control parameters. An amended continuous…
The limit of small entropy production is reached in relaxing systems long after preparation, and in stationary driven systems in the limit of small driving power. Surprisingly, for extended systems this limit is not in general the…
The wrapped normal distribution arises when a the density of a one-dimensional normal distribution is wrapped around the circle infinitely many times. At first look, evaluation of its probability density function appears tedious as an…
We consider the problem of the estimation of the invariant distribution function of an ergodic diffusion process when the drift coefficient is unknown. The empirical distribution function is a natural estimator which is unbiased, uniformly…
In this paper, three topics on semi-selfdecomposable distributions are studied. The first one is to characterize semi-selfdecomposable distributions by stochastic integrals with respect to Levy processes. This characterization defines a…
A parameter estimation problem for a class of semilinear stochastic evolution equations is considered. Conditions for consistency and asymptotic normality are given in terms of growth and continuity properties of the nonlinear part.…
The diffraction spectrum of coherent waves scattered from fractal supports is calculated exactly. The fractals considered are of the class generated iteratively by successive dilations and translations, and include generalizations of the…
Classical mathematical statistics deals with models that are parametrized by a Euclidean, i.e. finite dimensional, parameter. Quite often such models have been and still are chosen in practical situations for their mathematical simplicity…
We consider fractional diffusion equation with the distributed order Caputo derivative. We prove existence of a weak and regular solution for general uniformly elliptic operator under the assumption that the weight function is only…
Equilibrium statistical physics is considered from the point of view of statistical estimation theory. This involves the notions of statistical model, of estimators, and of exponential family. A useful property of the latter is the…
In this article we study the numerical approximation of a variable coefficient fractional diffusion equation. Using a change of variable, the variable coefficient fractional diffusion equation is transformed into a constant coefficient…
We construct the generalized entropy optimized by a given arbitrary statistical distribution with a finite linear expectation value of a random quantity of interest. This offers, via the maximum entropy principle, a unified basis for a…
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…
We review the class of species sampling models (SSM). In particular, we investigate the relation between the exchangeable partition probability function (EPPF) and the predictive probability function (PPF). It is straightforward to define a…
Nowadays, there is a series of complexities in biophysics that require a suitable approach to determine the measurable quantity. In this way, the superstatistics has been an important tool to investigate dynamic aspects of particles,…
Given a domain G, a reflection vector field d(.) on the boundary of G, and drift and dispersion coefficients b(.) and \sigma(.), let L be the usual second-order elliptic operator associated with b(.) and \sigma(.). Under suitable…
This work aims at making a comprehensive contribution in the general area of parametric inference for discretely observed diffusion processes. Established approaches for likelihood-based estimation invoke a time-discretisation scheme for…
In this paper we study the Exponentiated Hypoexponential Distribution with different parameters. The distribution added a parameter to the n parameters of the Hypoexponenial distribution. We first derive a closed expression of the…
We consider an optimal control problem that entails the minimization of a nondifferentiable cost functional, fractional diffusion as state equation and constraints on the control variable. We provide existence, uniqueness and regularity…
We present a formalism to calculate the probability distribution function of a scalar field coarse-grained over some spatial scales with a Gaussian filter at finite temperature. As an application, we investigate the role of subcritical…