Uniform almost sure convergence and asymptotic distribution of the wavelet-based estimators of partial derivatives of multivariate density function under weak dependence

2021 ◽  
pp. 1-27
Author(s):  
Soumaya Allaoui ◽  
Salim Bouzebda ◽  
Christophe Chesneau ◽  
Jicheng Liu
Keyword(s):  
Density Function ◽  
Asymptotic Distribution ◽  
Almost Sure Convergence ◽  
Weak Dependence ◽  
Partial Derivatives ◽  
Multivariate Density ◽  
Derivatives Of

scholarly journals Density Function of the FK4 Systematic Errors

1990 ◽  
Vol 141 ◽  
pp. 94-94
Author(s):  
V. S. Gubanov ◽  
N. I. Solina
Keyword(s):  
Density Function ◽  
Spherical Harmonics ◽  
Unit Sphere ◽  
Systematic Errors ◽  
Layer Potential ◽  
Partial Derivatives ◽  
Derivatives Of

A notion of density function of systematic errors of astrometric catalogues distributed on the unit sphere as a simple layer is introduced. Components of the catalogue errors in any direction are determined as partial derivatives of layer potential in the same direction. For example, the density function of FK4 errors is computed as an expansion of spherical harmonics.

Partial Derivatives of Regular Expressions over Alphabet-Invariant and User-Defined Labels

2019 ◽  
pp. 184-196 ◽  
Author(s):  
Stavros Konstantinidis ◽  
Nelma Moreira ◽  
João Pires ◽  
Rogério Reis
Keyword(s):  
Regular Expressions ◽  
Partial Derivatives ◽  
Derivatives Of

Partial Derivatives of the Lambert Problem

2014 ◽  
Author(s):  
Nitin Arora ◽  
Ryan P. Russell ◽  
Nathan J. Strange
Keyword(s):  
Partial Derivatives ◽  
Lambert Problem ◽  
Derivatives Of

Perturbation theory and finite Markov chains

1968 ◽  
Vol 5 (2) ◽  
pp. 401-413 ◽  
Author(s):  
Paul J. Schweitzer
Keyword(s):  
Perturbation Theory ◽  
Markov Chain ◽  
Markov Chains ◽  
Stationary Distribution ◽  
Fundamental Matrix ◽  
Transition Probabilities ◽  
Semi Group ◽  
Partial Derivatives ◽  
Finite Markov Chains ◽  
Derivatives Of

A perturbation formalism is presented which shows how the stationary distribution and fundamental matrix of a Markov chain containing a single irreducible set of states change as the transition probabilities vary. Expressions are given for the partial derivatives of the stationary distribution and fundamental matrix with respect to the transition probabilities. Semi-group properties of the generators of transformations from one Markov chain to another are investigated. It is shown that a perturbation formalism exists in the multiple subchain case if and only if the change in the transition probabilities does not alter the number of, or intermix the various subchains. The formalism is presented when this condition is satisfied.

scholarly journals ON A NONLOCAL PROBLEM FOR PARTIAL DIFFERENTIAL EQUATIONS OF PARABOLIC TYPE

2020 ◽  
Vol 8 (2) ◽  
pp. 24-39
Author(s):  
V. Gorodetskiy ◽  
R. Kolisnyk ◽  
O. Martynyuk
Keyword(s):  
Cauchy Problem ◽  
Fundamental Solution ◽  
Parabolic Type ◽  
Generalized Functions ◽  
Initial Condition ◽  
Partial Derivatives ◽  
Time Problem ◽  
The Cauchy Problem ◽  
Space Of Generalized Functions ◽  
Derivatives Of

Spaces of $S$ type, introduced by I.Gelfand and G.Shilov, as well as spaces of type $S'$, topologically conjugate with them, are natural sets of the initial data of the Cauchy problem for broad classes of equations with partial derivatives of finite and infinite orders, in which the solutions are integer functions over spatial variables. Functions from spaces of $S$ type on the real axis together with all their derivatives at $|x|\to \infty$ decrease faster than $\exp\{-a|x|^{1/\alpha}\}$, $\alpha > 0$, $a > 0$, $x\in \mathbb{R}$. The paper investigates a nonlocal multipoint by time problem for equations with partial derivatives of parabolic type in the case when the initial condition is given in a certain space of generalized functions of the ultradistribution type ($S'$ type). Moreover, results close to the Cauchy problem known in theory for such equations with an initial condition in the corresponding spaces of generalized functions of $S'$ type were obtained. The properties of the fundamental solution of a nonlocal multipoint by time problem are investigated, the correct solvability of the problem is proved, the image of the solution in the form of a convolution of the fundamental solution with the initial generalized function, which is an element of the space of generalized functions of $S'$ type.

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