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What is asymptotics?

What is asymptotics? Here are some definitions.

Noun
  1. (mathematics) asymptotic analysis
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Examples
The final chapter works with examples of stochastic process for LAN, LAMN, and LAQ type local asymptotics.
We shall look at the asymptotics of the barycentres of independent copies of Brownian motions on the hyperbolic spaces.

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