Almost sure convergence: Difference between revisions
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imported>Ragnar Schroder (→Important cases of almost sure convergence: added Mr Greg Woodhouse 's deleted example from main article.) |
imported>Ragnar Schroder m (Formatting) |
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'''Almost sure convergence''' is one of the 4 main modes of [[stochastic convergence]]. | '''Almost sure convergence''' is one of the 4 main modes of [[stochastic convergence]]. | ||
==Examples== | ==Examples== | ||
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===Intermediate example=== | ===Intermediate example=== | ||
==Definition== | ==Definition== | ||
==Important cases of almost sure convergence== | ==Important cases of almost sure convergence== | ||
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This is an example of the [[strong law of large numbers]]. | This is an example of the [[strong law of large numbers]]. | ||
==References== | ==References== | ||
==See also== | ==See also== | ||
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*[[Convergence in probability]] | *[[Convergence in probability]] | ||
*[[Convergence in rth order mean]] | *[[Convergence in rth order mean]] | ||
==Related topics== | ==Related topics== | ||
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*[[Stochastic process|Stochastic processes]] | *[[Stochastic process|Stochastic processes]] | ||
*[[Stochastic diffential equations]] | *[[Stochastic diffential equations]] | ||
==External links== | ==External links== | ||
[[Category:Mathematics Workgroup]] | [[Category:Mathematics Workgroup]] | ||
Revision as of 09:17, 5 July 2007
Almost sure convergence is one of the 4 main modes of stochastic convergence.
Examples
Basic example
Intermediate example
Definition
Important cases of almost sure convergence
If we flip a coin n times and record the percentage of times it comes up heads, the result will almost surely approach 50% as .
This is an example of the strong law of large numbers.
References
See also
- Stochastic convergence
- Convergence in distribution
- Convergence in probability
- Convergence in rth order mean
Related topics