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# Weak convergence of sums of moving averages
in the alpha-stable domain of attraction

**Florin Avram
**

Murad S. Taqqu

### Abstract:

*Skorohod has shown that the convergence of sums of i.i.d random variables
to an -stable Lévy motion, with , holds in the
weak- sense. is the commonly used Skorohod topology.
We show that for sums of moving averages with at least two
non-zero coefficients, weak- convergence cannot hold
because adjacent jumps of the process can coalesce in the
limit; however, if the
moving average coefficients are positive, then the adjacent
jumps are essentially monotone and one can have
weak- convergence. is weaker than , but it is strong
enough for the sup and inf functionals to be continuous.
*