Related papers: On the density of nonlinear statistics
We establish the density of the partial regularity result in the class of continuous viscosity solutions. Given a fully nonlinear equation, we prove the existence of a sequence entitled to the partial regularity result, approximating its…
Introducing the notion of a rational system of measure preserving transformations and proving a recurrence result for such systems, we give sufficient conditions in order a subset of rational numbers to contain arbitrary long arithmetic…
In this paper we deal with semilinear problems at resonance. We present a sufficient condition for the existence of a weak solution in terms of the asymptotic properties of nonlinearity. Our condition generalizes the classical…
This article is dedicated to the proof of the existence of classical solutions for a class of non-linear integral variational problems. Those problems are involved in nonlocal image and signal processing.
This note presents a new definition of nonlinear statistics mean and variance to simplify the nonlinear statistics computations. These concepts aim to provide a theoretical explanation of a novel nonlinear weighted residual methodology…
We extend the validity of a simple method for the existence of a density for stochastic differential equations, first introduced in [DebRom2014], by proving local estimate for the density, existence for the density with summable drift, and…
Physical systems that dissipate, mix and develop turbulence also irreversibly transport statistical density. In statistical physics, laws for these processes have a mathematical form and tractability that depends on whether the description…
In this paper, we study the global existence and regularity of H\"older continuous solutions for a series of nonlinear partial differential equations describing nonlinear waves.
This brief paper develops a probability density that models processes for which the physical mechanism is unknown. It has desirable properties which are not realized by densities derived from Gaussian process or other classic methods. In…
We introduce a notion of density which extends both the notion of Lelong number and the theory of intersection for positive closed currents on Kaehler manifolds. For arbitrary finite family of positive closed currents on a compact Kaehler…
The consistency of posterior distributions in density estimation is at the core of Bayesian statistical theory. Classical work established sufficient conditions, typically combining KL support with complexity bounds on sieves of high prior…
We show that hyperbolicity is a necessary condition for the well posedness of the noncharacteristic Cauchy problem for nonlinear partial differential equations. We give conditions on the initial data which are necessary for the existence of…
After a short discussion of the intimate relation between the generalized statistics and supersymmetry, we review the recent results on the nonlinear supersymmetry obtained in the context of the quantum anomaly problem and of the universal…
We consider the well-posedness of models involving age structure and non-linear diffusion. Such problems arise in the study of population dynamics. It is shown how diffusion and age boundary conditions can be treated that depend…
A nonlinear inequality is formulated in the paper. An estimate of the rate of growth/decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can…
A new version of a weak nonlinear law of large numbers proposed. The existence of the first moment for any summand is not assumed. The assumption of independence is understood in the nonlinear sense, and may be further a little relaxed.
A nonlinear inequality is formulated in the paper. An estimate of the rate of decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can be…
The concept of statistical convergence based on asymptotic density is introduced in this article through nets. Some possible extensions of classical results for statistical convergence of sequences are obtained in this article, with…
We study finitely additive extensions of the asymptotic density to all the subsets of natural numbers. Such measures are called density measures. We consider a class of density measures constructed from free ultrafilters on $\mathbb{N}$ and…
In stochastic decision problems, one often wants to estimate the underlying probability measure statistically, and then to use this estimate as a basis for decisions. We shall consider how the uncertainty in this estimation can be…