Stochastic approximation: Difference between revisions

Revision as of 00:02, 7 June 2011

Revision as of 00:03, 7 June 2011

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* <math>a_n</math> satisfies the following requirements <math>\qquad \sum^{\infty}_{i=0}a_i = \infty \quad </math> and <math>\quad \sum^{\infty}_{i=0}a^2_i < \infty \quad </math>

The last condition is fulfilled by taking <math>a_n=1a/n</math>, for <math> a > 0 </math> for example; other series are possible but in order to average out the noise in <math>N(x)</math>, <math>a_n</math> must converge slowly.

===Convergence Results===