strong law of large numbers
A sequence of random variables X1,X2,… with finite expectations
in a probability space
is said to satisfiy the strong law of large numbers
if
1nn∑k=1(Xk-E[Xk])a.s.→0, |
where a.s. stands for convergence almost surely.
When the random variables are identically distributed, with expectation μ, the law becomes:
1nn∑k=1Xka.s.→μ. |
Kolmogorov’s strong law of large numbers theorems give conditions on the random variables under which the law is satisfied.
Title | strong law of large numbers |
---|---|
Canonical name | StrongLawOfLargeNumbers |
Date of creation | 2013-03-22 13:13:10 |
Last modified on | 2013-03-22 13:13:10 |
Owner | Koro (127) |
Last modified by | Koro (127) |
Numerical id | 11 |
Author | Koro (127) |
Entry type | Definition |
Classification | msc 60F15 |
Related topic | MartingaleProofOfKolmogorovsStrongLawForSquareIntegrableVariables |