Pinning class of the Wiener measure by a functional: related martingales and invariance properties

2003 ◽  
Vol 127 (1) ◽  
pp. 1-36
Author(s):  
Fabrice Baudoin ◽  
Mich�le Thieullen
Keyword(s):  
Wiener Measure ◽  
Invariance Properties

Polar Decomposition of Wiener Measure and Schwarzian Integrals

2020 ◽  
Vol 41 (4) ◽  
pp. 709-713
Author(s):  
E. T. Shavgulidze ◽  
N. E. Shavgulidze
Keyword(s):  
Polar Decomposition ◽  
Wiener Measure

scholarly journals On a family of weighted convolution algebras

1990 ◽  
Vol 13 (3) ◽  
pp. 517-525 ◽  
Author(s):  
Hans G. Feichtinger ◽  
A. Turan Gürkanli
Keyword(s):  
Fourier Transforms ◽  
Locally Compact Abelian Group ◽  
Asymptotic Estimates ◽  
Locally Compact ◽  
Invariance Properties ◽  
Beurling Algebra ◽  
Convolution Algebras ◽  
Approximate Identities ◽  
Beurling Algebras ◽  
Banach Ideals

Continuing a line of research initiated by Larsen, Liu and Wang [12], Martin and Yap [13], Gürkanli [15], and influenced by Reiter's presentation of Beurling and Segal algebras in Reiter [2,10] this paper presents the study of a family of Banach ideals of Beurling algebrasLw1(G),Ga locally compact Abelian group. These spaces are defined by weightedLp-conditions of their Fourier transforms. In the first section invariance properties and asymptotic estimates for the translation and modulation operators are given. Using these it is possible to characterize inclusions in section 3 and to show that two spaces of this type coincide if and only if their parameters are equal. In section 4 the existence of approximate identities in these algebras is established, from which, among other consequences, the bijection between the closed ideals of these algebras and those of the corresponding Beurling algebra is derived.

scholarly journals Stochastic Order and Generalized Weighted Mean Invariance

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 662
Author(s):  
Mateu Sbert ◽  
Jordi Poch ◽  
Shuning Chen ◽  
Víctor Elvira
Keyword(s):  
Monte Carlo ◽  
Probability Distributions ◽  
Stochastic Order ◽  
Arithmetic Mean ◽  
Stochastic Orders ◽  
Arithmetic Means ◽  
Increasing Convex Order ◽  
Monte Carlo Techniques ◽  
Multiple Importance Sampling ◽  
Invariance Properties

In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series of numbers. The quasi-arithmetic mean, or Kolmogorov–Nagumo mean, generalizes the classical mean and appears in many disciplines, from information theory to physics, from economics to traffic flow. Stochastic orders are defined on weights (or equivalently, discrete probability distributions). They were introduced to study risk in economics and decision theory, and recently have found utility in Monte Carlo techniques and in image processing. We show in this paper that, if two distributions of weights are ordered under first stochastic order, then for any monotonic series of numbers their weighted quasi-arithmetic means share the same order. This means for instance that arithmetic and harmonic mean for two different distributions of weights always have to be aligned if the weights are stochastically ordered, this is, either both means increase or both decrease. We explore the invariance properties when convex (concave) functions define both the quasi-arithmetic mean and the series of numbers, we show its relationship with increasing concave order and increasing convex order, and we observe the important role played by a new defined mirror property of stochastic orders. We also give some applications to entropy and cross-entropy and present an example of multiple importance sampling Monte Carlo technique that illustrates the usefulness and transversality of our approach. Invariance theorems are useful when a system is represented by a set of quasi-arithmetic means and we want to change the distribution of weights so that all means evolve in the same direction.

Fractional convolution, fractional correlation and their translation invariance properties

2010 ◽  
Vol 90 (6) ◽  
pp. 1976-1984 ◽  
Author(s):  
Rafael Torres ◽  
Pierre Pellat-Finet ◽  
Yezid Torres
Keyword(s):  
Translation Invariance ◽  
Invariance Properties

scholarly journals CAN GENERAL RELATIVISTIC DESCRIPTION OF GRAVITATION BE CONSIDERED COMPLETE?

1998 ◽  
Vol 13 (17) ◽  
pp. 1393-1400 ◽  
Author(s):  
D. V. AHLUWALIA
Keyword(s):  
Solar System ◽  
Gravitational Potential ◽  
Invariance Properties ◽  
Planetary Orbits ◽  
Galactic Cluster ◽  
General Relativistic ◽  
Relativistic Description ◽  
Flavor Oscillation ◽  
Weak Fields ◽  
Great Attractor

The local galactic cluster, the Great attractor, embeds us in a dimensionless gravitational potential of about -3×10-5. In the solar system, this potential is constant to about 1 part in 1011. Consequently, planetary orbits, which are determined by the gradient in the gravitational potential, remain unaffected. However, this is not so for the recently introduced flavor-oscillation clocks where the new redshift-inducing phases depend on the gravitational potential itself. On these grounds, and by studying the invariance properties of the gravitational phenomenon in the weak fields, we argue that there exists an element of incompleteness in the general relativistic description of gravitation. An incompleteness-establishing inequality is derived and an experiment is outlined to test the thesis presented.

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