A functional limit theorem for random processes with immigration in the case of heavy tails

Alexander Marynych, Glib Verovkin

Let $(X_k,{\xi }_k{)}_{k\in \mathbb{N}}$ be a sequence of independent copies of a pair $(X,\xi )$ where $X$ is a random process with paths in the Skorokhod space $D[0,\infty )$ and $\xi$ is a…