Functional Convergence of Linear Processes with Heavy-Tailed Innovations

We study convergence in law of partial sums of linear processes with heavy-tailed innovations. In the case of summable coefficients, necessary and sufficient conditions for the finite dimensional convergence to an -stable L,vy Motion are given. The conditions lead to new, tractable sufficient conditions in the case . In the functional setting, we complement the existing results on -convergence, obtained for linear processes with nonnegative coefficients by Avram and Taqqu (Ann Probab 20:483-503, 1992) and improved by Louhichi and Rio (Electr J Probab 16(89), 2011), by proving that in the general setting partial sums of linear processes are convergent on the Skorokhod space equipped with the topology, introduced by Jakubowski (Electr J Probab 2(4), 1997).