Email this article A construction of reflecting Lévy processes
- Authors: Ibragimov I.A.1,2, Smorodina N.V.1,2, Faddeev M.M.1,2
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Affiliations:
- Steklov Mathematical Institute of Russian Academy of Sciences at Saint-Peterburg
- Saint-Petersburg State University
- Issue: Vol 484, No 5 (2019)
- Pages: 523-526
- Section: Mathematics
- URL: https://journals.eco-vector.com/0869-5652/article/view/12759
- DOI: https://doi.org/10.31857/S0869-56524845523-526
- ID: 12759
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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
Academician of the RAS
Russian Federation, 27, Fontanka, Saint-Petersburg, 191011; 7/9, Universitetskaya embankment, Saint-Petersburg, 199034N. 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
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- Pilipenko A. An Introduction to Stochastic Differential Equations with Reflection. Potsdam: Universitatsverlag, 2014.
- Ибрагимов И. А., Смородина Н.В., Фаддеев М.М. // Теория вероятностей и ее применения. 2016. Т. 61. № 4. С. 733–752.
- Ибрагимов И.А., Смородина Н.В., Фаддеев М.М. // Теория вероятностей и ее применения. 2017. Т. 62. № 3. С. 446–467.
- Ито К., Маккин Г. Диффузионные процессы и их траектории М.: Мир, 1968
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