Search results
Results From The WOW.Com Content Network
Prokhorov's theorem can be extended to consider complex measures or finite signed measures. Theorem: Suppose that ( S , ρ ) {\displaystyle (S,\rho )} is a complete separable metric space and Π {\displaystyle \Pi } is a family of Borel complex measures on S {\displaystyle S} .
Yuri Vasilyevich Prokhorov (Russian: Ю́рий Васи́льевич Про́хоров; 15 December 1929 – 16 July 2013) was a Soviet and Russian mathematician, active in the field of probability theory. He was a PhD student of Andrey Kolmogorov at the Moscow State University, where he obtained his PhD in 1956. Prokhorov became a ...
In mathematics, the Lévy–Prokhorov metric (sometimes known just as the Prokhorov metric) is a metric (i.e., a definition of distance) on the collection of probability measures on a given metric space. It is named after the French mathematician Paul Lévy and the Soviet mathematician Yuri Vasilyevich Prokhorov; Prokhorov introduced it in 1956 ...
Tightness and convergence. Tightness is often a necessary criterion for proving the weak convergence of a sequence of probability measures, especially when the measure space has infinite dimension. See. Finite-dimensional distribution. Prokhorov's theorem. Lévy–Prokhorov metric. Weak convergence of measures. Tightness in classical Wiener space.
Lévy metric. In mathematics, the Lévy metric is a metric on the space of cumulative distribution functions of one-dimensional random variables. It is a special case of the Lévy–Prokhorov metric, and is named after the French mathematician Paul Lévy .
Chebyshev. Georg Cantor, inventor of set theory. Cantor was born into the Russian Empire, moving to Saxony with his family at age 11. Sergey Chaplygin, author of Chaplygin's equation important in aerodynamics and notion of Chaplygin gas. Nikolai Chebotaryov, author of Chebotarev's density theorem.
Fano variety. In algebraic geometry, a Fano variety, introduced by Gino Fano in (Fano 1934, 1942), is an algebraic variety that generalizes certain aspects of complete intersections of algebraic hypersurfaces whose sum of degrees is at most the total dimension of the ambient projective space. Such complete intersections have important ...
The mathematical theory, combining probability and functional analysis, was first developed in the 1950s by Skorokhod and Prokhorov, but was regarded as a specialized advanced topic. This book's contribution was a self-contained treatment at a useful basic level of abstraction, that of Polish space .