Probability and Measure, Anniversary ed

Billingsley, P. (2012). Probability and Measure, Anniversary ed. Wiley.

Type

Book

Intellectual base

Textbook

Year

2012

Pages cited

1-3

ISBN

9781118122372

Link

https://openlibrary.org/books/OL25254284Mmatched

Cited by

2 citations across 2 artifacts.

Domain-specific

• Collectively exhaustive events
  • The move from For a six-sided die, the events even outcome and odd outcome are collectively exhaustive and mutually exclusive. to The events at least one component fails and all components succeed are collectively exhaustive for a declared system trial. demonstrates that continuity.
• Reflection principle (Wiener process)
  • The move from For \(a>0\), the principle gives \(\Pr(\sup_{0\leq s\leq t}W_s\geq a)=2\Pr(W_t\geq a)\). to The distribution of the first hitting time of a positive level can be obtained from the complementary distribution of the running maximum. demonstrates that continuity.

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