A Construction of Reflecting Lévy Processes


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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.

About the authors

I. A. Ibragimov

St. Petersburg Department, Steklov Mathematical Institute, Russian Academy of Sciences; St. Petersburg State University

Author for correspondence.
Email: ibr32@pdmi.ras.ru
Russian Federation, St. Petersburg, 191023; St. Petersburg, 199034

N. V. Smorodina

St. Petersburg Department, Steklov Mathematical Institute, Russian Academy of Sciences; St. Petersburg State University

Author for correspondence.
Email: smorodina@pdmi.ras.ru
Russian Federation, St. Petersburg, 191023; St. Petersburg, 199034

M. M. Faddeev

St. Petersburg Department, Steklov Mathematical Institute, Russian Academy of Sciences; St. Petersburg State University

Author for correspondence.
Email: m.faddeev@spbu.ru
Russian Federation, St. Petersburg, 191023; St. Petersburg, 199034

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