Exact lower and upper bounds for shifts of Gaussian measures

@article{Pinelis2022ExactLA,
  title={Exact lower and upper bounds for shifts of Gaussian measures},
  author={Iosif Pinelis},
  journal={Teoriya Veroyatnostei i ee Primeneniya},
  year={2022}
}
  • 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… 

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