Avram, FlorinTaqqu, Murad S.2018-09-052018-09-051992-01-01F. Avram, M.S. Taqqu. 1992. "Weak Convergence of Sums of Moving Averages in the α -Stable Domain of Attraction." The Annals of Probability, Volume 20, Issue 1, pp. 483 - 503 (21). https://doi.org/10.1214/aop/11769899380091-1798https://hdl.handle.net/2144/31176Skorohod has shown that the convergence of sums of i.i.d. random variables to an a-stable Levy motion, with 0 < a < 2, holds in the weak-J1 sense. J1 is the commonly used Skorohod topology. We show that for sums of moving averages with at least two nonzero coefficients, weak-J1 conver- gence 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-M1 con- vergence. M1 is weaker than J1, but it is strong enough for the sup and inf functionals to be continuous.483 - 503 (21)© 1992 Institute of Mathematical StatisticsScience & technologyPhysical sciencesStatistics & probabilityMathematicsTopological theoremsStaircasesPerceptron convergence procedureMathematical theoremsCounterexamplesStochastic processesStatisticsArticle0000-0002-1145-9082 (TAQQU, MS)