Lyapunov Condition
المؤلف:
Ash, R. B. and Doléans-Dade, C. A.
المصدر:
Probability & Measure Theory, 2nd ed. New York: Academic Press
الجزء والصفحة:
...
24-4-2021
2080
Lyapunov Condition
The Lyapunov condition, sometimes known as Lyapunov's central limit theorem, states that if the 
th moment (with 
) exists for a statistical distribution of independent random variates 
(which need not necessarily be from same distribution), the means 
and variances 
are finite, and
 |
(1)
|
then if
 |
(2)
|
where
 |
(3)
|
the central limit theorem holds.
REFERENCES:
Ash, R. B. and Doléans-Dade, C. A. Probability & Measure Theory, 2nd ed. New York: Academic Press, p. 307, 1999.
Billingsley, P. Probability and Measure, 2nd ed. New York: p. 371, Wiley, 1986.
Resnik, S. A Probability Path. Boston, MA: Birkhäuser, p. 319, 1999.
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