Geodesic
Convoluted Brownian motion: a semimartingale approach
Teoriâ slučajnyh processov, Tome 21 (2016) no. 2, pp. 58-83.

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: Periodic Gaussian process, periodic Ornstein-Uhlenbeck process, Markov-field property
Mots-clés : enlargement of filtration. 
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Sylvie Rœlly; Pierre Vallois. Convoluted Brownian motion: a semimartingale approach. Teoriâ slučajnyh processov, Tome 21 (2016) no. 2, pp. 58-83. http://geodesic.mathdoc.fr/item/THSP_2016_21_2_a5/

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