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convergence with probability one

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  • Probability theory — is the branch of mathematics concerned with analysis of random phenomena.[1] The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non deterministic events or measured… …   Wikipedia

  • Convergence of random variables — In probability theory, there exist several different notions of convergence of random variables. The convergence of sequences of random variables to some limit random variable is an important concept in probability theory, and its applications to …   Wikipedia

  • Convergence of measures — In mathematics, more specifically measure theory, there are various notions of the convergence of measures. Three of the most common notions of convergence are described below. Contents 1 Total variation convergence of measures 2 Strong… …   Wikipedia

  • Probability of default — Basel II Bank for International Settlements Basel Accords Basel I Basel II Background Banking Monetary policy Central bank Risk …   Wikipedia

  • probability theory — Math., Statistics. the theory of analyzing and making statements concerning the probability of the occurrence of uncertain events. Cf. probability (def. 4). [1830 40] * * * Branch of mathematics that deals with analysis of random events.… …   Universalium

  • Probability-generating function — In probability theory, the probability generating function of a discrete random variable is a power series representation (the generating function) of the probability mass function of the random variable. Probability generating functions are… …   Wikipedia

  • One-shot learning — is an object categorization problem of current research interest in computer vision. Whereas most machine learning based object categorization algorithms require training on hundreds or thousands of images and very large datasets, one shot… …   Wikipedia

  • Doob's martingale convergence theorems — In mathematics specifically, in stochastic analysis Doob s martingale convergence theorems are a collection of results on the long time limits of supermartingales, named after the American mathematician Joseph Leo Doob. Contents 1 Statement of… …   Wikipedia

  • Characteristic function (probability theory) — The characteristic function of a uniform U(–1,1) random variable. This function is real valued because it corresponds to a random variable that is symmetric around the origin; however in general case characteristic functions may be complex valued …   Wikipedia

  • Martingale (probability theory) — For the martingale betting strategy , see martingale (betting system). Stopped Brownian motion is an example of a martingale. It can be used to model an even coin toss betting game with the possibility of bankruptcy. In probability theory, a… …   Wikipedia

  • Standard probability space — In probability theory, a standard probability space (called also Lebesgue Rokhlin probability space) is a probability space satisfying certain assumptions introduced by Vladimir Rokhlin in 1940 [1] . He showed that the unit interval endowed with… …   Wikipedia

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