TY  - INPR
A1  - Roelly, Sylvie
A1  - Vallois, Pierre
T1  - Convoluted Brownian motion
BT  - a semimartingale approach
N2  - 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 neither
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 higher-dimensional monomial convoluted Brownian motion.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 5 (2016) 9 
KW  - periodic Gaussian process
KW  - periodic Ornstein-Uhlenbeck process
KW  - Markov-field property
KW  - enlargement of filtration
Y1  - 2016
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-96339
SN  - 2193-6943
VL  - 5
IS  - 9
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  -