A Construction of Reflecting Lévy Processes

Academician of the RAS I. A. Ibragimov^a^,^b^,*, N. V. Smorodina^a^,^b^,**, and M. M. Faddeev^a^,^b^,***
Translated by I. Ruzanova

^aSt. Petersburg Department, Steklov Mathematical Institute, Russian Academy of Sciences, St. Petersburg, 191023 Russia

^bSt. Petersburg State University, St. Petersburg, 199034 Russia

Correspondence to: *e-mail: ibr32@pdmi.ras.ru
Correspondence to: **e-mail: smorodina@pdmi.ras.ru
Correspondence to: ***e-mail: m.faddeev@spbu.ru

Received 2 October, 2018

Abstract—For some classes of Lévy processes, the notion of reflection from an interval boundary is introduced. It is shown that trajectories of a reflecting process define random operators that map functions defined on the interval boundaries into elements of ${{L}_{2}}$ on the whole interval.

DOI: 10.1134/S1064562419010228