Finding the closest probabilistic Parseval frame in the 2-Wasserstein metric

Abstract In this article, we present the Laguerre wavelet exact Parseval frame method (LWPM) for the two-dimensional flow of a rotating micropolar fluid in a porous channel with huge mass transfer. This flow is governed by highly nonlinear coupled partial differential equations (PDEs) are reduced to the nonlinear coupled ordinary differential equations (ODEs) using Berman's similarity transformation before being solved numerically by a Laguerre wavelet exact Parseval frame method. We also compared this work with the other methods in the literature available. Moreover, in the graphs of the velocity distribution and microrotation, we shown that the proposed scheme's solutions are more accurate and applicable than other existing methods in the literature. Numerical results explaining the effects of various physical parameters connected with the flow are discussed.

Download Full-text

Curvature of the Manifold of Fixed-Rank Positive-Semidefinite Matrices Endowed with the Bures–Wasserstein Metric

Lecture Notes in Computer Science - Geometric Science of Information ◽

10.1007/978-3-030-26980-7_77 ◽

2019 ◽

pp. 739-748 ◽

Cited By ~ 1

Author(s):

Estelle Massart ◽

Julien M. Hendrickx ◽

P.-A. Absil

Keyword(s):

Positive Semidefinite ◽

Wasserstein Metric ◽

Positive Semidefinite Matrices ◽

Fixed Rank

Download Full-text

Compound Poisson approximation for the distribution of extremes

Advances in Applied Probability ◽

10.1239/aap/1019160958 ◽

2002 ◽

Vol 34 (1) ◽

pp. 223-240 ◽

Cited By ~ 8

Author(s):

A. D. Barbour ◽

S. Y. Novak ◽

A. Xia

Keyword(s):

Point Processes ◽

Poisson Approximation ◽

Value Theory ◽

Wasserstein Metric ◽

Compound Poisson ◽

Compound Poisson Approximation ◽

Limiting Behaviour ◽

Explicit Bounds ◽

Empirical Point ◽

Poisson Cluster

Empirical point processes of exceedances play an important role in extreme value theory, and their limiting behaviour has been extensively studied. Here, we provide explicit bounds on the accuracy of approximating an exceedance process by a compound Poisson or Poisson cluster process, in terms of a Wasserstein metric that is generally more suitable for the purpose than the total variation metric. The bounds only involve properties of the finite, empirical sequence that is under consideration, and not of any limiting process. The argument uses Bernstein blocks and Lindeberg's method of compositions.

Download Full-text