Functional convergence for moving averages with heavy tails and random coefficients

We study functional convergence of sums of moving averages with random coefficients and heavy-tailed innovations. Under some standard moment conditions and the assumption that all partial sums of the series of coefficients are a.s. bounded between zero and the sum of the series we obtain functional convergence of the corresponding partial sum stochastic process in the space $D[0,1]$ of c\`{a}dl\`{a}g functions with the Skorohod $M_{2}$ topology.