“Blumenthal's zero–one law”的意思、由来-开放百科全书

词条

Blumenthal's zero–one law

释义

Statement
References

In the mathematical theory of probability, Blumenthal's zero–one law,^[1] named after Robert McCallum Blumenthal, is a statement about the nature of the beginnings of memoryless processes. Loosely, it states that any stochastic process on with the strong Markov property has an essentially deterministic starting point.

Statement

Suppose that is a stochastic process on a probability space with , natural filtration and canonical identification . If has the strong Markov property then any event in the germ sigma algebra has either or ^[2]

References

1. ^{{Citation | last = Blumenthal | first = Robert M. | title = An extended Markov property | journal = Transactions of the American Mathematical Society | volume = 85 | issue = 1 | pages = 52–72 | year = 1957 | jstor = 1992961 | doi = 10.2307/1992961 | mr = 0088102 | zbl = 0084.13602}}
2. ^{{Citation|title=Diffusions, Markov Processes, and Martingales|last=Rogers|first=L. C. G.|last2=Williams|first2=D.|publisher=Cambridge University Press|year=2000|isbn=978-0521775946|location=|pages=23, §I.12|oclc=42874839}}

1 : Probability theory

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