scholarly journals A general convergence result for the Ricci flow in higher dimensions

2008 ◽  
Vol 145 (3) ◽  
pp. 585-601 ◽  
Author(s):  
Simon Brendle
Keyword(s):  
Ricci Flow ◽  
Higher Dimensions ◽  
Convergence Result ◽  
General Convergence

scholarly journals Convergence rates for estimators of geodesic distances and Frèchet expectations

2018 ◽  
Vol 55 (4) ◽  
pp. 1001-1013
Author(s):  
Catherine Aaron ◽  
Olivier Bodart
Keyword(s):  
Probability Distribution ◽  
Convergence Rate ◽  
Compact Manifold ◽  
Convergence Rates ◽  
Geodesic Distance ◽  
Convergence Result ◽  
Regularity Conditions ◽  
Compact Set ◽  
Geodesic Distances ◽  
General Convergence

Abstract Consider a sample 𝒳n={X1,…,Xn} of independent and identically distributed variables drawn with a probability distribution ℙX supported on a compact set M⊂ℝd. In this paper we mainly deal with the study of a natural estimator for the geodesic distance on M. Under rather general geometric assumptions on M, we prove a general convergence result. Assuming M to be a compact manifold of known dimension d′≤d, and under regularity assumptions on ℙX, we give an explicit convergence rate. In the case when M has no boundary, knowledge of the dimension d′ is not needed to obtain this convergence rate. The second part of the work consists in building an estimator for the Fréchet expectations on M, and proving its convergence under regularity conditions, applying the previous results.

scholarly journals Pyramid Ricci flow in higher dimensions

2020 ◽  
Vol 296 (1-2) ◽  
pp. 511-523 ◽  
Author(s):  
Andrew D. McLeod ◽  
Peter M. Topping
Keyword(s):  
Ricci Flow ◽  
Higher Dimensions

scholarly journals Strong convergence of multivariate maxima

2020 ◽  
Vol 57 (1) ◽  
pp. 314-331
Author(s):  
Michael Falk ◽  
Simone A. Padoan ◽  
Stefano Rizzelli
Keyword(s):  
Strong Convergence ◽  
Higher Dimensions ◽  
Convergence Result ◽  
Common Distribution ◽  
Convergence Results ◽  
Negative Exponential Distribution ◽  
Common Distribution Function ◽  
Variation Distance ◽  
Negative Exponential ◽  
Variational Distance

AbstractIt is well known and readily seen that the maximum of n independent and uniformly on [0, 1] distributed random variables, suitably standardised, converges in total variation distance, as n increases, to the standard negative exponential distribution. We extend this result to higher dimensions by considering copulas. We show that the strong convergence result holds for copulas that are in a differential neighbourhood of a multivariate generalised Pareto copula. Sklar’s theorem then implies convergence in variational distance of the maximum of n independent and identically distributed random vectors with arbitrary common distribution function and (under conditions on the marginals) of its appropriately normalised version. We illustrate how these convergence results can be exploited to establish the almost-sure consistency of some estimation procedures for max-stable models, using sample maxima.

scholarly journals A General Convergence Result for Particle Filtering

2011 ◽  
Vol 59 (7) ◽  
pp. 3424-3429 ◽  
Author(s):  
Xiao-Li Hu ◽  
Thomas B. Schon ◽  
Lennart Ljung
Keyword(s):  
Particle Filtering ◽  
Convergence Result ◽  
General Convergence

scholarly journals A general convergence theorem for multiple-set split feasibility problem in Hilbert spaces

2015 ◽  
Vol 31 (3) ◽  
pp. 349-357
Author(s):  
ABDUL RAHIM KHAN ◽  
◽  
MUJAHID ABBAS ◽  
YEKINI SHEHU ◽  
◽  
...  
Keyword(s):  
Strong Convergence ◽  
Hilbert Spaces ◽  
Convergence Theorem ◽  
Split Feasibility Problem ◽  
Contractive Mapping ◽  
Convergence Result ◽  
Feasibility Problem ◽  
Infinite Dimensional ◽  
Split Feasibility ◽  
General Convergence

We establish strong convergence result of split feasibility problem for a family of quasi-nonexpansive multi-valued mappings and a total asymptotically strict pseudo-contractive mapping in infinite dimensional Hilbert spaces.

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