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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.
Download QR code; Print/export Download as PDF; Printable version; In other projects ... In mathematics and statistics, the continuity theorem may refer to one of the ...
Martingale central limit theorem; Infinite divisibility (probability) Method of moments (probability theory) Stability (probability) Stein's lemma; Characteristic function (probability theory) Lévy continuity theorem; Darmois–Skitovich theorem; Edgeworth series; Helly–Bray theorem; Kac–Bernstein theorem; Location parameter; Maxwell's theorem
Continuous stochastic process: the question of continuity of a stochastic process is essentially a question of convergence, and many of the same concepts and relationships used above apply to the continuity question. Asymptotic distribution; Big O in probability notation; Skorokhod's representation theorem; The Tweedie convergence theorem ...
Lévy was born in Paris to a Jewish family which already included several mathematicians. [3] His father Lucien Lévy was an examiner at the École Polytechnique.Lévy attended the École Polytechnique and published his first paper in 1905, at the age of nineteen, while still an undergraduate, in which he introduced the Lévy–Steinitz theorem.
Lévy's continuity theorem; Lévy distribution; Lévy flight; Lévy metric; Lévy process; Lévy skew alpha-stable distribution; Lévy–Prokhorov metric; Lévy's constant; Lévy's stochastic area; Lévy's zero-one law
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 ...