On a scale function for testing the conformality of a Finsler manifold to a Berwald manifold

AbstractWe show that geodesic random walks on a complete Finsler manifold of bounded geometry converge to a diffusion process which is, up to a drift, the Brownian motion corresponding to a Riemannian metric.

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On a robust local estimator for the scale function in heteroscedastic nonparametric regression

Statistics & Probability Letters ◽

10.1016/j.spl.2010.03.015 ◽

2010 ◽

Vol 80 (15-16) ◽

pp. 1185-1195 ◽

Cited By ~ 9

Author(s):

Graciela Boente ◽

Marcelo Ruiz ◽

Ruben H. Zamar

Keyword(s):

Nonparametric Regression ◽

Scale Function

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Evaluating Scale Functions of Spectrally Negative Lévy Processes

Journal of Applied Probability ◽

10.1017/s0021900200004010 ◽

2008 ◽

Vol 45 (01) ◽

pp. 135-149 ◽

Cited By ~ 10

Author(s):

B. A. Surya

Keyword(s):

Numerical Method ◽

Numerical Computation ◽

Numerical Algorithm ◽

Levy Process ◽

Scale Function ◽

Esscher Transform ◽

Change Of Measure ◽

Scale Functions ◽

Spectrally Negative Lévy Process ◽

Spectrally Negative Lévy Processes

In this paper we present a robust numerical method to compute the scale function W (q)(x) of a general spectrally negative Lévy process (X, P). The method is based on the Esscher transform of measure Pν under which X is taken and the scale function is determined. This change of measure makes it possible for the scale function to be bounded and, hence, makes numerical computation easy, fast, and stable. Working under the new measure Pν and using the method of Abate and Whitt (1992) and Choudhury, Lucantoni, and Whitt (1994), we give a fast stable numerical algorithm for the computation of W (q)(x).

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Autoparallel Deviation in the Geometry of Lyra

Canadian Mathematical Bulletin ◽

10.4153/cmb-1960-033-8 ◽

1960 ◽

Vol 3 (3) ◽

pp. 263-271 ◽

Cited By ~ 1

Author(s):

J. R. Vanstone

Keyword(s):

Riemannian Manifold ◽

Euclidean Space ◽

Calculus Of Variations ◽

Finsler Manifold ◽

Geometrical Approach ◽

Second Variation ◽

Geodesic Deviation ◽

The Difference ◽

The Second Variation

One of the fruitful tools for examining the properties of a Riemannian manifold is the study of “geodesic deviation”. The manner in which a vector, representing the displacement between points on two neighbouring geodesies, behaves gives an indication of the difference between the manifold and an Euclidean space. The study is essentially a geometrical approach to the second variation of the lengthintegral in the calculus of variations [1]. Similar considerations apply in the geometry of Lyra [2] but as we shall see, appropriate analytical modifications must be made. The approach given here is modelled after that of Rund [3] which was originally designed to deal with a Finsler manifold but which applies equally well to the present case.

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A Certain Class of Relatively Equi-Statistical Fuzzy Approximation Theorems

European Journal of Pure and Applied Mathematics ◽

10.29020/nybg.ejpam.v13i5.3711 ◽

2020 ◽

Vol 13 (5) ◽

pp. 1212-1230

Author(s):

Susanta Kumar Paikray ◽

Priyadarsini Parida ◽

S. A. Mohiuddine

Keyword(s):

Statistical Convergence ◽

Type Theorem ◽

Point Of View ◽

Scale Function ◽

Korovkin Type Theorem ◽

Approximation Theorems ◽

Fuzzy Approximation ◽

Inclusion Relations ◽

Korovkin Type Theorems ◽

Sequence Of Functions

The aim of this paper is to introduce the notions of relatively deferred Nörlund uniform statistical convergence as well as relatively deferred Norlund point-wise statistical convergence through the dierence operator of fractional order of fuzzy-number-valued sequence of functions, and a type of convergence which lies between aforesaid notions, namely, relatively deferred Nörlund equi-statistical convergence. Also, we investigate the inclusion relations among these aforesaidnotions. As an application point of view, we establish a fuzzy approximation (Korovkin-type) theorem by using our new notion of relatively deferred Norlund equi-statistical convergence and intimate that this result is a non-trivial generalization of several well-established fuzzy Korovkin-type theorems which were presented in earlier works. Moreover, we estimate the fuzzy rate of the relatively deferred Nörlund equi-statistical convergence involving a non-zero scale function by using the fuzzy modulus of continuity.

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