Geometry of moment spaces

1953 ◽  
Vol 0 (12) ◽  
pp. 0-0 ◽  
Author(s):  
S. Karlin ◽  
L. S. Shapley
Keyword(s):  
Moment Spaces

Moment Spaces and Resonance Theorems

Inequalities ◽  
1965 ◽  
pp. 97-131
Author(s):  
Edwin F. Beckenbach ◽  
Richard Bellman
Keyword(s):  
Moment Spaces

scholarly journals Large Deviations on Moment Spaces

2005 ◽  
Vol 10 (0) ◽  
pp. 662-690 ◽  
Author(s):  
Li-Vang Lozada-Chang
Keyword(s):  
Large Deviations ◽  
Moment Spaces

More bounds on the expectation of a convex function of a random variable

1972 ◽  
Vol 9 (4) ◽  
pp. 803-812 ◽  
Author(s):  
Ben-Tal A. ◽  
E. Hochman
Keyword(s):  
Convex Function ◽  
Upper Bound ◽  
Random Variable ◽  
Independent Random Variables ◽  
Multivariate Distributions ◽  
Absolute Deviation ◽  
Additional Information ◽  
Wait And See ◽  
The Mean ◽  
Moment Spaces

Jensen gave a lower bound to Eρ(T), where ρ is a convex function of the random vector T. Madansky has obtained an upper bound via the theory of moment spaces of multivariate distributions. In particular, Madansky's upper bound is given explicitly when the components of T are independent random variables. For this case, lower and upper bounds are obtained in the paper, which uses additional information on T rather than its mean (mainly its expected absolute deviation about the mean) and hence gets closer to Eρ(T).The importance of having improved bounds is illustrated through a nonlinear programming problem with stochastic objective function, known as the “wait and see” problem.

More bounds on the expectation of a convex function of a random variable

1972 ◽  
Vol 9 (04) ◽  
pp. 803-812 ◽  
Author(s):  
Ben-Tal A. ◽  
E. Hochman
Keyword(s):  
Convex Function ◽  
Upper Bound ◽  
Random Variable ◽  
Independent Random Variables ◽  
Multivariate Distributions ◽  
Absolute Deviation ◽  
Additional Information ◽  
Wait And See ◽  
The Mean ◽  
Moment Spaces

Jensen gave a lower bound to Eρ(T), where ρ is a convex function of the random vector T. Madansky has obtained an upper bound via the theory of moment spaces of multivariate distributions. In particular, Madansky's upper bound is given explicitly when the components of T are independent random variables. For this case, lower and upper bounds are obtained in the paper, which uses additional information on T rather than its mean (mainly its expected absolute deviation about the mean) and hence gets closer to Eρ(T). The importance of having improved bounds is illustrated through a nonlinear programming problem with stochastic objective function, known as the “wait and see” problem.

scholarly journals Distributions on matrix moment spaces

2014 ◽  
Vol 131 ◽  
pp. 17-31
Author(s):  
Holger Dette ◽  
Matthias Guhlich ◽  
Jan Nagel
Keyword(s):  
Moment Spaces ◽  
Matrix Moment

scholarly journals The Exponential Premium Calculation Principle Revisited

1999 ◽  
Vol 29 (2) ◽  
pp. 215-226 ◽  
Author(s):  
Michel Denuit
Keyword(s):  
Premium Calculation ◽  
Moment Spaces

AbstractIn this paper, it is shown how to approximate theoretical premium calculation principles in order to make them useful in practice. The method relies on stochastic extrema in moment spaces and is illustrated with the aid of the exponential principle.

Moment spaces and inequalities

1953 ◽  
Vol 20 (2) ◽  
pp. 261-271 ◽  
Author(s):  
Melvin Dresher
Keyword(s):  
Moment Spaces

scholarly journals Impact of collision models on the physical properties and the stability of lattice Boltzmann methods

2020 ◽  
Vol 378 (2175) ◽  
pp. 20190397 ◽  
Author(s):  
C. Coreixas ◽  
G. Wissocq ◽  
B. Chopard ◽  
J. Latt
Keyword(s):  
Physical Properties ◽  
Lattice Boltzmann ◽  
Soft Matter ◽  
Spectral Element ◽  
Collision Model ◽  
Zero Viscosity Limit ◽  
High Reynolds ◽  
Bgk Approximation ◽  
Moment Spaces ◽  
Collision Models

The lattice Boltzmann method (LBM) is known to suffer from stability issues when the collision model relies on the BGK approximation, especially in the zero viscosity limit and for non-vanishing Mach numbers. To tackle this problem, two kinds of solutions were proposed in the literature. They consist in changing either the numerical discretization (finite-volume, finite-difference, spectral-element, etc.) of the discrete velocity Boltzmann equation (DVBE), or the collision model. In this work, the latter solution is investigated in detail. More precisely, we propose a comprehensive comparison of (static relaxation time based) collision models, in terms of stability, and with preliminary results on their accuracy, for the simulation of isothermal high-Reynolds number flows in the (weakly) compressible regime. It starts by investigating the possible impact of collision models on the macroscopic behaviour of stream-and-collide based D2Q9-LBMs, which clarifies the exact physical properties of collision models on LBMs. It is followed by extensive linear and numerical stability analyses, supplemented with an accuracy study based on the transport of vortical structures over long distances. In order to draw conclusions as generally as possible, the most common moment spaces (raw, central, Hermite, central Hermite and cumulant), as well as regularized approaches, are considered for the comparative studies. LBMs based on dynamic collision mechanisms (entropic collision, subgrid-scale models, explicit filtering, etc.) are also briefly discussed. This article is part of the theme issue ‘Fluid dynamics, soft matter and complex systems: recent results and new methods’.

Moment Spaces and Resonance Theorems

Inequalities ◽  
1965 ◽  
pp. 97-131
Author(s):  
Edwin F. Beckenbach ◽  
Richard Bellman
Keyword(s):  
Moment Spaces
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