Exact lower and upper bounds for shifts of Gaussian measures

  title={Exact lower and upper bounds for shifts of Gaussian measures},
  author={Iosif Pinelis},
  journal={Teoriya Veroyatnostei i ee Primeneniya},
  • I. Pinelis
  • Published 19 May 2022
  • Mathematics
  • Teoriya Veroyatnostei i ee Primeneniya
Получены точные верхние и нижние грани для отношения $\operatorname{\mathbf E}w(\mathbf X-\mathbf v)/\operatorname{\mathbf E}w(\mathbf X)$ для центрированного гауссовского случайного вектора $\mathbf X$ в $\mathbf R^n$, а также оценки скорости изменения $\operatorname{\mathbf E}w(\mathbf X-t\mathbf v)$ по отношению к $t$, где $w\colon\mathbf R^n\to[0,\infty)$ - произвольная одновершинная функция и $\mathbf v$ - произвольный вектор в $\mathbf R^n… 


Real Analysis
– Weierstrass Theorem Theorem If f is a continuous real-valued function on [a, b] and if any is given, then there exists a polynomial p on [a, b] s.t. |f(x)− p(x)| < for all x ∈ [a, b]. In other
On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
We extend the Prekopa-Leindler theorem to other types of convex combinations of two positive functions and we strengthen the Prekopa—Leindler and Brunn-Minkowski theorems by introducing the notion of
On l'Hospital-type rules for monotonicity.
Elsewhere we developed rules for the monotonicity pattern of the ratio r := f/g of two differentiable functions on an interval (a,b) based on the monotonicity pattern of the ratio := f 0 /g 0 of the
The Brunn-Minkowski inequality
In 1978, Osserman [124] wrote an extensive survey on the isoperimetric inequality. The Brunn-Minkowski inequality can be proved in a page, yet quickly yields the classical isoperimetric inequality
Majorization in Multivariate Distributions
Convex analysis, Princeton Landmarks in Mathematics
  • 1997
Folland , Real analysis , Pure and Applied Mathematics ( New York ) , John Wiley & Sons Inc . , New York , 1984 , Modern techniques and their applications , A Wiley - Interscience Publication
    Real analysis, Pure and Applied Mathematics (New York)
    • MR MR767633
    • 1984