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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.
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 ...
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 ...
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. [note 1] It is a special case of the inverse-gamma distribution.
In mathematics and statistics, the continuity theorem may refer to one of the following results: the Lévy continuity theorem on random variables;
Lévy's modulus of continuity theorem is a theorem that gives a result about an almost sure behaviour of an estimate of the modulus of continuity for Wiener process, that is used to model what's known as Brownian motion. Lévy's modulus of continuity theorem is named after the French mathematician Paul Lévy.
In mathematics Lévy's constant (sometimes known as the Khinchin–Lévy constant) occurs in an expression for the asymptotic behaviour of the denominators of the convergents of simple continued fractions. [1]
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.