Brownian motion in certain symmetric spaces and nonnegative eigenfunctions of the Laplace-Beltrami operator

1968 ◽  
pp. 203-228 ◽  
Author(s):  
E. B. Dynkin
Keyword(s):  
Brownian Motion ◽  
Symmetric Spaces ◽  
Beltrami Operator

$L^p - L^q$ estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. I

1993 ◽  
Vol 72 (1) ◽  
pp. 109-150 ◽  
Author(s):  
Michael Cowling ◽  
Saverio Giulini ◽  
Stefano Meda
Keyword(s):  
Symmetric Spaces ◽  
Beltrami Operator

scholarly journals On the projections of Laplacians under Riemannian submersions

2001 ◽  
Vol 25 (1) ◽  
pp. 33-42
Author(s):  
Huiling Le
Keyword(s):  
Brownian Motion ◽  
Riemannian Manifold ◽  
Differential Operator ◽  
Riemannian Submersion ◽  
Beltrami Operator ◽  
Riemannian Submersions

We give a condition on Riemannian submersions from a Riemannian manifoldMto a Riemannian manifoldNwhich will ensure that it induces a differential operator onNfrom the Laplace-Beltrami operator onM. Equivalently, this condition ensures that a Riemannian submersion maps Brownian motion to a diffusion.

Supersymmetry

2018 ◽  
Author(s):  
Arno Kuijlaars
Keyword(s):  
Brownian Motion ◽  
Random Matrices ◽  
Generating Functions ◽  
Symmetric Spaces ◽  
Ensemble Average ◽  
Alternative Representation ◽  
Non Linear

This article examines conceptual and structural issues related to supersymmetry. It first provides an overview of generating functions before discussing supermathematics, with a focus on Grassmann or anticommuting variables, vectors and matrices, groups and symmetric spaces, and derivatives and integrals. It then considers various applications of supersymmetry to random matrices, such as the representation of the ensemble average and the Hubbard–Stratonovich transformation, along with its generalization and superbosonization. It also describes matrix δ functions and an alternative representation as well as important and technically challenging problems that supersymmetry addresses beyond the invariant and factorizing ensembles. The article concludes with an analysis of the supersymmetric non-linear σ model, Brownian motion in superspace, circular ensembles and the Colour-Flavour-Transformation.

scholarly journals $L^p-L^q$ estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. III

2001 ◽  
Vol 51 (4) ◽  
pp. 1047-1069 ◽  
Author(s):  
Michael Cowling ◽  
Saverio Giulini ◽  
Stefano Meda
Keyword(s):  
Symmetric Spaces ◽  
Beltrami Operator

Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

2007 ◽  
Vol 44 (02) ◽  
pp. 393-408 ◽  
Author(s):  
Allan Sly
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
White Noise ◽  
Gaussian Process ◽  
Discrete Data ◽  
Hölder Exponent ◽  
Scaling Properties ◽  
Multifractional Brownian Motion ◽  
Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

Brownian motion with quadratic killing and some implications

1986 ◽  
Vol 23 (04) ◽  
pp. 893-903 ◽  
Author(s):  
Michael L. Wenocur
Keyword(s):  
Brownian Motion ◽  
Weibull Distribution ◽  
Special Function ◽  
Function Theory ◽  
Killing Rate

Brownian motion subject to a quadratic killing rate and its connection with the Weibull distribution is analyzed. The distribution obtained for the process killing time significantly generalizes the Weibull. The derivation involves the use of the Karhunen–Loève expansion for Brownian motion, special function theory, and the calculus of residues.

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