Generalization of the Prokhorov multidimensional analog of the Chebyshev inequality

• Date: 2006
• Main Authors: Sokolov, N. V., Соколов, Н. В.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2006
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3476
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We prove two theorems on upper and lower bounds for probabilities in the multidimensional case. We generalize and improve the Prokhorov multidimensional analog of the Chebyshev inequality and establish a multidimensional analog of the generalized Kolmogorov probability estimate.