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convergence of a sequence with finite upcrossings
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(Theorem)
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The following result characterizes convergence of a sequence in terms of finiteness of numbers of upcrossings.
Since the number of upcrossings $U[a,b]$ differs from the number of downcrossings $D[a,b]$ by at most one, the theorem can equivalently be stated in terms of the finiteness of $D[a,b]$
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"convergence of a sequence with finite upcrossings" is owned by gel.
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Cross-references: downcrossings, number, extended real numbers, converges, real numbers, upcrossings, sequence
This is version 1 of convergence of a sequence with finite upcrossings, born on 2009-02-15.
Object id is 11630, canonical name is ConvergenceOfASequenceWithFiniteUpcrossings.
Accessed 337 times total.
Classification:
| AMS MSC: | 60G17 (Probability theory and stochastic processes :: Stochastic processes :: Sample path properties) | | | 40A05 (Sequences, series, summability :: Convergence and divergence of infinite limiting processes :: Convergence and divergence of series and sequences) |
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Pending Errata and Addenda
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