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  - 
TY  - INPR
A1  - Dereudre, David
A1  - Mazzonetto, Sara
A1  - Roelly, Sylvie
T1  - Exact simulation of Brownian diffusions with drift admitting jumps
N2  - Using an algorithm based on a retrospective rejection sampling scheme, we propose an exact simulation of a Brownian diffusion whose drift admits several jumps. We treat explicitly and extensively the case of two jumps, providing numerical simulations. Our main contribution is to manage the technical difficulty due to the presence of two jumps thanks to a new explicit expression of the transition density of the skew Brownian motion with two semipermeable barriers and a constant drift.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 5 (2016) 7 
KW  - exact simulation method
KW  - skew Brownian motion
KW  - skew diffusion
KW  - Brownian motion with discontinuous drift
Y1  - 2016
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-91049
SN  - 2193-6943
VL  - 5
IS  - 7
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Cattiaux, Patrick
A1  - Fradon, Myriam
A1  - Kulik, Alexei M.
A1  - Roelly, Sylvie
T1  - Long time behavior of stochastic hard ball systems
JF  - Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability
N2  - We study the long time behavior of a system of n = 2, 3 Brownian hard balls, living in R-d for d >= 2, submitted to a mutual attraction and to elastic collisions.
KW  - hard core interaction
KW  - local time
KW  - Lyapunov function
KW  - normal reflection
KW  - Poincare inequality
KW  - reversible measure
KW  - stochastic differential equations
Y1  - 2016
U6  - https://doi.org/10.3150/14-BEJ672
SN  - 1350-7265
SN  - 1573-9759
VL  - 22
SP  - 681
EP  - 710
PB  - International Statistical Institute
CY  - Voorburg
ER  -