Strong Law of Large Numbers

  • Thread starter jetoso
  • Start date
73
0
For the Strong Law of Large Numbers, as far as I know it applies when, let say, the random variables {Xn: n=1,2,...} are iid, hence uncorrelated, their second moments have a common bound and they have a finite mean mu.
What else I must consider? Is there anyother consideretion or case when the SLLN does not apply?
 

mathman

Science Advisor
7,652
378
There are weaker conditions for the strong law to hold.

For example, the Kolmogoroff Criterion does not require the distributions be identical.
It needs sum (Vk/k2) be a convergent series (V=variance).

Alternatively if the distributions are identical, all you need is the mean - the variance may be infinite.
 

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top