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 operator that map functions defined on the interval boundaries into elements of L2 on the whole interval.


About the authors

I. A. Ibragimov

Steklov Mathematical Institute of Russian Academy of Sciences at Saint-Peterburg; Saint-Petersburg State University

Author for correspondence.
Email: ibr32@pdmi.ras.ru

Russian Federation, 27, Fontanka, Saint-Petersburg, 191011; 7/9, Universitetskaya embankment, Saint-Petersburg, 199034

Academician of the RAS

N. V. Smorodina

Steklov Mathematical Institute of Russian Academy of Sciences at Saint-Peterburg; Saint-Petersburg State University

Email: smorodina@pdmi.ras.ru

Russian Federation, 27, Fontanka, Saint-Petersburg, 191011; 7/9, Universitetskaya embankment, Saint-Petersburg, 199034

M. M. Faddeev

Steklov Mathematical Institute of Russian Academy of Sciences at Saint-Peterburg; Saint-Petersburg State University

Email: m.faddeev@spbu.ru

Russian Federation, 27, Fontanka, Saint-Petersburg, 191011; 7/9, Universitetskaya embankment, Saint-Petersburg, 199034

References

  1. Скороход А.В. // Теория вероятностей и ее применения. 1961. Т. 6. № 3. С. 287–298.
  2. Pilipenko A. An Introduction to Stochastic Differential Equations with Reflection. Potsdam: Universitatsverlag, 2014.
  3. Ибрагимов И. А., Смородина Н.В., Фаддеев М.М. // Теория вероятностей и ее применения. 2016. Т. 61. № 4. С. 733–752.
  4. Ибрагимов И.А., Смородина Н.В., Фаддеев М.М. // Теория вероятностей и ее применения. 2017. Т. 62. № 3. С. 446–467.
  5. Ито К., Маккин Г. Диффузионные процессы и их траектории М.: Мир, 1968

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