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[[Category:Theorems in probability theory]] ...

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[[Category:Theorems in probability theory]] ...

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* [[Central limit theorem]], in probability theory * [[Edgeworth's limit theorem]], in economics ...

{{Short description|Result in probability theory}} In [[probability theory]], '''Lévy’s continuity theorem''', or '''Lévy's convergence theorem''',<re ...

...ted sequence <math>\{X_t, \mathcal{F}_t\}_{-\infty}^{\infty}</math> on a [[probability space]] <math>(\Omega, \mathcal{F}, \mathbb{P})</math>. <math>X_t</math> is ...ce than [[independence (probability theory)|independence]], yet most limit theorems that hold for an independent sequence will also hold for an MDS. ...

...tion|Relates tightness of measures to relative compactness in the space of probability measures}} ...n [[Yuri Vasilevich Prokhorov|Yuri Vasilyevich Prokhorov]], who considered probability measures on complete separable metric spaces. The term "Prokhorov’s theorem ...

{{Short description|Theorem in probability theory}} ...tration]] generated by a [[Wiener process|Brownian motion]] can be written in terms of an [[Itô integral]] with respect to this Brownian motion. ...

...y be decomposed in a unique way as the sum of a [[Martingale (probability theory)|martingale]] and an [[increasing process|increasing]] [[predictable proces ...as the Doob-Meyer decomposition.<ref>Meyer 1962</ref><ref>Meyer 1963</ref> In honor of Doob, Meyer used the term "class D" to refer to the class of super ...

{{Short description|1=Overview of and topical guide to probability}} {{Probability topics sidebar}} ...

{{Short description|Probability theorem}} In [[probability theory]], '''Le Cam's theorem''', named after [[Lucien Le Cam]], states the follow ...

'''Statistical regularity''' is a notion in [[statistics]] and [[probability theory]] that random events exhibit regularity when repeated enough times or that ...ographic statistics]], [[quality control]] of a manufacturing process, and in many other parts of our lives. ...

...obability theory]], the '''Helly–Bray theorem''' relates the [[convergence in distribution|weak convergence]] of [[cumulative distribution function]]s to ...eorem holds. Let ''P'' and ''P''₁, ''P''₂, ... be [[probability measure]]s on some [[Set (mathematics)|set]] ''S''. Then ''P''<sub>''n''</ ...

{{Short description|Theorem in probability theory}} ...thur S. |last=Goldberger |author-link=Arthur Goldberger |title=Econometric Theory |location=New York |publisher=Wiley |year=1964 |pages=[https://archive.org/ ...

...a geometrical space invariant under the [[symmetry group]] of that space. In more recent times, the meaning has been broadened to include a view of inva ...ntegralgeometrie'', [[VEB Deutscher Verlag der Wissenschaften]]</ref> was in this connection. It follows from the [[Crofton formula|classic theorem of C ...

{{Short description|Measure theory and probability theorem}} ...ath> It is used as a type of [[transfinite induction]] to prove many other theorems, such as [[Fubini's theorem]]. ...

...t <math>E_1</math> occurs before <math>E_2</math> equals the [[conditional probability]] that <math>E_1</math> occurs given that <math>E_1</math> or <math>E_2</ma ...ellette|title=The Calculus Diaries: How Math Can Help You Lose Weight, Win in Vegas, and Survive a Zombie Apocalypse|url=https://books.google.com/books?i ...

...urnal |last=Cramér |first=H. |last2=Wold |first2=H. |date=1936 |title=Some Theorems on Distribution Functions |url=http://doi.wiley.com/10.1112/jlms/s1-11.4.29 ...h> [[Convergence_of_random_variables#Convergence_in_distribution|converges in distribution]] to <math> {X} </math> if and only if: ...

...asure]] on a [[separable space|separable]] [[Banach space]]. It was proved in the 1970s by [[Gopinath Kallianpur|Kallianpur]]&ndash;Satô&ndash;Stefan and ...ble Banach space is an [[abstract Wiener space | abstract Wiener measure]] in the sense of [[Leonard Gross | L. Gross]]". The result by Dudley et al. gen ...