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Convoluted Brownian motion: a semimartingale approach
Sylvie Rœllya, Pierre Valloisb a Universität Potsdam, Institut für Mathematik, Karl-Liebknecht-Str. 24-25, 14476 Potsdam OT Golm, Germany
b Universitacuté de Lorraine, Institut de Mathématiques Elie Cartan, INRIA-BIGS, CNRS UMR 7502, BP 239, 54506 Vanduvre-lès-Nancy Cedex, France
Аннотация:
In this paper we analyse semimartingale properties of a class of Gaussian periodic processes, called convoluted Brownian motions, obtained by convolution between a deterministic function and a Brownian motion. A classical example in this class is the periodic Ornstein-Uhlenbeck process. We compute their characteristics and show that in general, they are never Markovian nor satisfy a time-Markov field property. Nevertheless, by enlargement of filtration and/or addition of a one-dimensional component, one can in some case recover the Markovianity. We treat exhaustively the case of the bidimensional trigonometric convoluted Brownian motion and the multidimensional monomial convoluted Brownian motion.
Ключевые слова:
Periodic Gaussian process, periodic Ornstein-Uhlenbeck process, Markov-field property, enlargement of filtration.
Образец цитирования:
Sylvie Rœlly, Pierre Vallois, “Convoluted Brownian motion: a semimartingale approach”, Theory Stoch. Process., 21(37):2 (2016), 58–83
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/thsp162 https://www.mathnet.ru/rus/thsp/v21/i2/p58
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Страница аннотации: | 119 | PDF полного текста: | 41 | Список литературы: | 22 |
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