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Sard's approximation processes and oblique projections

G. Corach, J. I. Giribet, A. Maestripieri (2009)

Studia Mathematica

Three problems arising in approximation theory are studied. These problems have already been studied by Arthur Sard. The main goal of this paper is to use geometrical compatibility theory to extend Sard's results and get characterizations of the sets of solutions.

Self-stabilizing processes: uniqueness problem for stationary measures and convergence rate in the small-noise limit

Samuel Herrmann, Julian Tugaut (2012)

ESAIM: Probability and Statistics

In the context of self-stabilizing processes, that is processes attracted by their own law, living in a potential landscape, we investigate different properties of the invariant measures. The interaction between the process and its law leads to nonlinear stochastic differential equations. In [S. Herrmann and J. Tugaut. Electron. J. Probab. 15 (2010) 2087–2116], the authors proved that, for linear interaction and under suitable conditions, there exists a unique symmetric limit measure associated...

Self-stabilizing processes: uniqueness problem for stationary measures and convergence rate in the small-noise limit

Samuel Herrmann, Julian Tugaut (2012)

ESAIM: Probability and Statistics

In the context of self-stabilizing processes, that is processes attracted by their own law, living in a potential landscape, we investigate different properties of the invariant measures. The interaction between the process and its law leads to nonlinear stochastic differential equations. In [S. Herrmann and J. Tugaut. Electron. J. Probab. 15 (2010) 2087–2116], the authors proved that, for linear interaction and under suitable conditions, there...

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