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In probability theory, Lévy’s continuity theorem, or Lévy's convergence theorem, [1] named after the French mathematician Paul Lévy, connects convergence in distribution of the sequence of random variables with pointwise convergence of their characteristic functions.
The characteristic function approach is particularly useful in analysis of linear combinations of independent random variables: a classical proof of the Central Limit Theorem uses characteristic functions and Lévy's continuity theorem. Another important application is to the theory of the decomposability of random variables.
Lévy’s continuity theorem: The sequence {X n} converges in distribution to X if and only if the sequence of corresponding characteristic functions {φ n} converges pointwise to the characteristic function φ of X. Convergence in distribution is metrizable by the Lévy–Prokhorov metric.
In probability theory, a Lévy process, named after the French mathematician Paul Lévy, is a stochastic process with independent, stationary increments: it represents the motion of a point whose successive displacements are random, in which displacements in pairwise disjoint time intervals are independent, and displacements in different time intervals of the same length have identical ...
Download QR code; Print/export Download as PDF; Printable version; ... In mathematics and statistics, the continuity theorem may refer to one of the following results:
In probability theory and statistics, the Lévy distribution, named after Paul Lévy, is a continuous probability distribution for a non-negative random variable.In spectroscopy, this distribution, with frequency as the dependent variable, is known as a van der Waals profile.
Download QR code; Print/export Download as PDF; ... Lévy's modulus of continuity theorem This page was last edited on 7 April 2024, at 15:12 (UTC). Text ...
Continuity (fiction), consistency of plot elements, such as characterization, location, and costuming, within a work of fiction (this is a mass noun) Continuity (setting) , one of several similar but distinct fictional universes in a broad franchise of related works (this is a count noun)