Fluctuations of homogeneous processes with independent increments

This is the author's abstract of a thesis presented for the academic degree of Doctor of Physicomathematical Sciences. The thesis has been defended on December 21, 1970 at the Council which awards academic degrees in mechanomathematical sciences at Novosibirsk State University. The official opponents were V. M. Zolotarev (Doctor of Physicomathematical Sciences), V. S. Korolyuk (Doctor of Physicomathematical Sciences and Corresponding member of the Academy of Sciences of the Ukrainian SSR), and Yu. V. Prokhorov (Doctor of Physicomathematical Sciences and Corresponding Member of the Academy of Sciences of the USSR).