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Concentration Inequalities for Euler Schemes
2006We establish a Poincare inequality for the law at time t of the explicit Euler scheme for a stochastic differential equation. When the diffusion coefficient is constant, we also establish a Logarithmic Sobolev inequality for both the explicit and implicit Euler scheme, with a constant related to the convexity of the drift coefficient.
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Wasserstein-Divergence transportation inequalities and polynomial concentration inequalities
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Concentration inequalities for sums
2015This chapter is devoted to concentration inequalities for sums or functions of independent random variables. We will give a survey of known results as well as new extensions in this area.
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Concentration inequalities and logarithmic Sobolev inequalities
2009We first derive concentration inequalities based on the logarithmic Sobolev inequality and then give some generic and classical examples of laws that satisfy this inequality. Since we shall use it in these notes for Wigner’s matrices, we focus first on concentration for laws in RN.
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Concentration inequalities for martingales
2015This chapter is devoted to concentration inequalities for martingales such as Azuma-Hoeffding, Freedman, and De la Pena inequalities. Several extensions will also be provided. In particular, we will focus our attention on improved versions of Azuma-Hoeffding and Freedman’s type inequalities.
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Inequalities for Concentration of a Decomposition
Theory of Probability & Its Applications, 1994Summary: For a measure \(P\) defined on the \(\sigma\)-algebra \(B\) of Borel sets of the real line with Lebesgue measure \(L\), the concentration functions \[ Q(P,z) = \sup_{x \in R} {\mathbf P} ([x,x + z)),\qquad \widehat{Q}(P,z) = \sup\{ {\mathbf P}(A): L(A) \leq z,\;A \in {\mathcal B}\} \] and the concentration function of the decomposition ...
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Did Concentration Increase Inequality?
2013AbstractAfter presenting independent evidence of a weakened working class and a resurgent capitalist class in chapter 2, chapter 3 attempts to link these two up. An aggressive process of concentration in business through ‘downsize and distribute’ involved steps like union busting, labour-displacing technical change, and greater incentive to top ...
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