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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 statistics and stochastic processes. The same concepts are known in more general mathematics as stochastic convergence and they formalize the idea that a sequence of essentially random or unpredictable events can sometimes be expected to settle down into a behaviour that is essentially unchanging when items far enough into the sequence are studied. The different possible notions of convergence relate to how such a behaviour can be characterised: two readily understood behaviours are that the sequence eventually takes a constant value, and that val

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  • Convergence of random variables
  • Konvergenz (Stochastik)
  • Convergence de variables aléatoires
  • Convergenza di variabili casuali
  • 確率変数の収束
  • Zbieżność według rozkładu
  • Convergentie (kansrekening)
  • Convergência de variáveis aleatórias
  • Сходимость по распределению
  • 随机变量的收敛
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  • In der Stochastik existieren verschiedene Konzepte eines Grenzwertbegriffs für Zufallsvariablen. Anders als im Fall reeller Zahlenfolgen gibt es keine natürliche Definition für das Grenzverhalten von Zufallsvariablen bei wachsendem Stichprobenumfang, weil das asymptotische Verhalten der Experimente immer von den einzelnen Realisationen abhängt und wir es also formal mit der Konvergenz von Funktionen zu tun haben. Daher haben sich im Laufe der Zeit unterschiedlich starke Konzepte herausgebildet, die wichtigsten dieser Konvergenzarten werden im Folgenden kurz vorgestellt.
  • Zbieżność według rozkładu – jeden z rodzajów zbieżności wektorów losowych, nazywany czasem słabą zbieżnością.
  • 数学の確率論の分野において、確率変数の収束(かくりつへんすうのしゅうそく、英: convergence of random variables)に関しては、いくつかの異なる概念がある。確率変数列のある極限への収束は、確率論や、その応用としての統計学や確率過程の研究における重要な概念の一つである。より一般的な数学において同様の概念は確率収束(stochastic convergence)として知られ、その概念は、本質的にランダムあるいは予測不可能な事象の列は、その列から十分離れているアイテムを研究する場合において、しばしば、本質的に不変な挙動へと落ち着くことが予想されることがある、という考えを定式化するものである。異なる収束の概念とは、そのような挙動の特徴づけに関連するものである:すぐに分かる二つの挙動とは、その列が最終的に定数となるか、あるいはその列に含まれる値は変動を続けるがある不変な確率分布によってその変動が表現される、というようなものである。
  • Сходи́мость по распределе́нию в теории вероятностей — вид сходимости случайных величин.
  • In de kansrekening kan convergentie van een rij stochastische variabelen verschillende betekenissen hebben. Anders dan bij rijen getallen is er geen voor de hand liggende definitie voor het asymptotische gedrag bij toenemende omvang van de steekproef. Daardoor zijn er verschillende convergentiebegrippen ontstaan, van verschillende sterkte. De belangrijkste daarvan worden in dit lemma besproken. Het gaat steeds om een rij stochastische variabelen , gedefinieerd op een kansruimte
  • 正如一个数列可能收敛到某个极限量,一列函数可能收敛到某个极限函数一样,随机收敛指的是一系列随机变量 在n趋向于无穷大时,会越来越接近某个固定的极限。这个极限可能是指: 1. * 趋向某个固定的数; 2. * 趋向某个确定函数的输出值; 3. * 的概率分布越来越接近某个特定的随机变量的概率分布; 4. * 和某个特定随机变量的差别的平均值(数学期望值)趋向于0; 5. * 和某个特定随机变量的差别的方差趋向于0. 等等。这些不同的极限的定义,可以严格地写成不同的收敛方式的定义。
  • 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 statistics and stochastic processes. The same concepts are known in more general mathematics as stochastic convergence and they formalize the idea that a sequence of essentially random or unpredictable events can sometimes be expected to settle down into a behaviour that is essentially unchanging when items far enough into the sequence are studied. The different possible notions of convergence relate to how such a behaviour can be characterised: two readily understood behaviours are that the sequence eventually takes a constant value, and that val
  • In teoria della probabilità e statistica è molto vivo il problema di studiare fenomeni con comportamento incognito ma, nei grandi numeri, riconducibili a fenomeni noti e ben studiati. A ciò vengono in soccorso i vari teoremi di convergenza di variabili casuali, che appunto studiano le condizioni sotto cui certe successioni di variabili casuali di una certa distribuzione tendono ad altre distribuzioni.
  • Dans la théorie des probabilités, il existe différentes notions de convergence de variables aléatoires. La convergence (dans un des sens décrits ci-dessous) de suites de variables aléatoires est un concept important de la théorie des probabilités utilisé notamment en statistique et dans l'étude des processus stochastiques. Par exemple, la moyenne de n variables aléatoires indépendantes et identiquement distribuées converge presque sûrement vers l'espérance commune de ces variables aléatoires (si celle-ci existe).Ce résultat est connu sous le nom de loi forte des grands nombres. .
  • Em probabilidade, existem diferentes conceitos de convergência de variáveis aleatórias. A convergência de uma sequência de variáveis aleatórias para algum limite é um conceito importante da teoria das probabilidades, com aplicações em estatística e processos estocásticos. Por exemplo, a média de n variáveis aleatórias não correlacionadas Yi, i = 1, …, n, é dada por: Outros conceitos são usados em outros teoremas, como o importante teorema do limite central.
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