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添加3字节 、 2020年10月17日 (六) 13:18
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and the ''n''-fold convolution <math>F^{*n}</math> is defined inductively by the rule:
 
and the ''n''-fold convolution <math>F^{*n}</math> is defined inductively by the rule:
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n倍卷积<math>F^{*n}</math>定义如下:
 
n倍卷积<math>F^{*n}</math>定义如下:
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The tail distribution function <math>\overline{F}</math> is defined as <math>\overline{F}(x) = 1-F(x)</math>.
 
The tail distribution function <math>\overline{F}</math> is defined as <math>\overline{F}(x) = 1-F(x)</math>.
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尾分布函数<math>\overline{F}</math>定义为<math>\overline{F}(x) = 1-F(x)</math>。
    
A distribution <math>F</math> on the positive half-line is subexponential<ref name="Asmussen"/><ref>{{Cite web|url=https://www.researchgate.net/publication/242637603_A_Theorem_on_Sums_of_Independent_Positive_Random_Variables_and_Its_Applications_to_Branching_Random_Processes|title=A Theorem on Sums of Independent Positive Random Variables and Its Applications to Branching Random Processes|last=Chistyakov|first=V. P.|date=1964|website=ResearchGate|language=en|archive-url=|archive-date=|access-date=April 7, 2019}}</ref><ref>{{Cite web|url=https://projecteuclid.org/download/pdf_1/euclid.aop/1176996225|title=The Class of Subexponential Distributions|last=Teugels|first=Jozef L.|authorlink=|date=1975|website=|publisher=Annals of Probability|publication-place=[[KU Leuven|University of Louvain]]|archive-url=|archive-date=|access-date=April 7, 2019}}</ref> if
 
A distribution <math>F</math> on the positive half-line is subexponential<ref name="Asmussen"/><ref>{{Cite web|url=https://www.researchgate.net/publication/242637603_A_Theorem_on_Sums_of_Independent_Positive_Random_Variables_and_Its_Applications_to_Branching_Random_Processes|title=A Theorem on Sums of Independent Positive Random Variables and Its Applications to Branching Random Processes|last=Chistyakov|first=V. P.|date=1964|website=ResearchGate|language=en|archive-url=|archive-date=|access-date=April 7, 2019}}</ref><ref>{{Cite web|url=https://projecteuclid.org/download/pdf_1/euclid.aop/1176996225|title=The Class of Subexponential Distributions|last=Teugels|first=Jozef L.|authorlink=|date=1975|website=|publisher=Annals of Probability|publication-place=[[KU Leuven|University of Louvain]]|archive-url=|archive-date=|access-date=April 7, 2019}}</ref> if
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尾分布函数<math>\overline{F}</math>定义为<math>\overline{F}(x) = 1-F(x)</math>。
   
如果满足以下条件,则正半线上的分布<math>F</math>为次指数:
 
如果满足以下条件,则正半线上的分布<math>F</math>为次指数:
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This implies<ref name="Embrechts">{{cite book |author1=Embrechts P. |author2=Klueppelberg C. |author3=Mikosch T. |title=Modelling extremal events for insurance and finance |publisher=Springer | series = Stochastic Modelling and Applied Probability|location=Berlin |year=1997  | volume=33| doi = 10.1007/978-3-642-33483-2|isbn=978-3-642-08242-9 }}</ref> that, for any <math>n \geq 1</math>,
 
This implies<ref name="Embrechts">{{cite book |author1=Embrechts P. |author2=Klueppelberg C. |author3=Mikosch T. |title=Modelling extremal events for insurance and finance |publisher=Springer | series = Stochastic Modelling and Applied Probability|location=Berlin |year=1997  | volume=33| doi = 10.1007/978-3-642-33483-2|isbn=978-3-642-08242-9 }}</ref> that, for any <math>n \geq 1</math>,
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这蕴含着,对于任何<math>n \geq 1</math>,
 
这蕴含着,对于任何<math>n \geq 1</math>,
  
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