In this paper we prove a strong approximation result for a mixing sequence with infinite variance and logarithmic decay rate of the mixing coefficient. The result is proved under the assumption that the distribution is symmetric and lies in the domain of attraction of the normal law. Moreover the truncated variance function is supposed to be slowly varying with log-log type remainder.
Raluca Balan. Ingrid-Mona Zamfirescu. "Strong Approximation for Mixing Sequences with Infinite Variance." Electron. Commun. Probab. 11 11 - 23, 2006. https://doi.org/10.1214/ECP.v11-1175