1. Instytut Matematyczny, Uniwersytet Wroc?awski, Pl. Grunwaldzki 2/4, 50-384, Wroc?aw, Poland;2. Wydzia? Matematyki, Politechnika Wroc?awska, Wyb. Wyspiańskiego 27, 50-370, Wroc?aw, Poland
Abstract:
We consider a random walk which is obtained from the simple random walk by a discrete time version of Bochner’s subordination. We prove that under certain conditions on the subordinator appropriately scaled random walk converges in the Skorohod space to the symmetric -stable process . We also prove asymptotic formula for the transition function of similar to the Pólya’s asymptotic formula for .