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Extend the Borel-Cantelli lemma to sequences of non-independent random variables
Borel-cantelli Lemma Cauchy-schwarz Inequality
2010/9/21
In this paper we discus on the Borel-Cantelli lemma when the condition of independent events is replaced by negative quadrant dependent condition.
Current fluctuations for independent random walks in multiple dimensions
Independent random walks hydrodynamic limit current Independent random walks
2010/12/6
Consider a system of particles evolving as independent and iden-tically distributed (i.i.d.) random walks. Initial fluctuations in the particle density get translated over time with velocity ~v, the c...
Symmetry analysis of three dimensional time independent Schrodinger-Newton equation
Integration Lie algebras Nonlinear Partial Differential Equations
2010/9/10
Schr¨odinger-Newton (SN) equations are modifications of the Schr¨odinger equation proposed by Roger Penrose involved in a gravitationally-induced wave function collapse scheme. In this paper, the thre...
Fuzzy local ICA for extracting independent components related to external criteria
fuzzy clustering independent component analysis
2010/9/10
Independent component analysis (ICA) is an unsupervised technique for blind source separation, and the ICA algorithms using nongaussianity as the measure of mutual independence have been also used for...
On Some New Retard Integral Inequalities in $n$ Independent Variables and Their Applications
Retard integral inequalities integral equation Partial differential equation
2008/6/27
In this paper, we established some retard integral inequalities in n independent variables and by means of examples we show the usefulness of our results.