Central limit theorem#Lyapunov CLT

The Lyapunov condition is next to the Lindeberg condition one of the two typical conditions on a sequence of random variables to prove a classical central limit theorem in the stochastic. It goes back to the Russian mathematician Aleksandr Mikhailovich Lyapunov.

Formulation

Be a sequence of stochastically independent random variables with and for all. In addition, the sum of the variances of the call.

The sequence of random variables of the Lyapunov condition iff is now sufficient if

.

From the Lyapunov condition follows the Lindeberg condition, and it can show the validity of the central limit theorem for.

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