Back Élément aléatoire French 確率要素 Japanese Случайный элемент Russian Випадковий елемент Ukrainian 随机元素 Chinese
In probability theory, random element is a generalization of the concept of random variable to more complicated spaces than the simple real line. The concept was introduced by Maurice Fréchet (1948) who commented that the “development of probability theory and expansion of area of its applications have led to necessity to pass from schemes where (random) outcomes of experiments can be described by number or a finite set of numbers, to schemes where outcomes of experiments represent, for example, vectors, functions, processes, fields, series, transformations, and also sets or collections of sets.”[1]
The modern-day usage of “random element” frequently assumes the space of values is a topological vector space, often a Banach or Hilbert space with a specified natural sigma algebra of subsets.[2]
- ^ Fréchet, M. (1948). "Les éléments aléatoires de nature quelconque dans un espace distancié". Annales de l'Institut Henri Poincaré. 10 (4): 215–310.
- ^ V.V. Buldygin, A.B. Kharazishvili. Geometric Aspects of Probability Theory and Mathematical Statistics. – Kluwer Academic Publishers, Dordrecht. – 2000