Skorokhod

Skorokhod is a Slavic surname. In mathematics, it is chiefly associated with a Soviet probabilist whose work on stochastic processes gave rise to several central concepts in probability theory. The Skorokhod representation theorem provides a mechanism to realize weak convergence of probability measures on a metric space as almost sure convergence of random variables defined on a common probability space. The Skorokhod embedding problem asks for a stopping time of Brownian motion that yields any prescribed distribution, a problem that has inspired many constructions and related results.

Skorokhod space refers to the function space D[0,1], the set of cadlag functions (right-continuous with left limits) equipped with a topology, now known as the Skorokhod topology. This topology, notably the J1 variant, is central to the study of convergence in distribution for stochastic processes and underpins many functional limit theorems. The Skorokhod problem, or Skorokhod reflection problem, describes how to constrain processes to remain in a domain by a minimal nondecreasing process that pushes the path back at the boundary.

The name Skorokhod thus appears in a range of mathematical concepts tied to work in probability theory and stochastic processes. It is also a surname of Slavic origin borne by other scholars and, in various countries, by institutions and places named in honor of the mathematician. In general, Skorokhod denotes both a surname and a family of mathematical notions associated with his contributions.