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  - Keller, Peter
T1  - Mathematical modeling of molecular motors
N2  - Amongst the many complex processes taking place in living cells, transport of cargoes across the cytosceleton is fundamental to cell viability and activity. To move cargoes between the different cell parts, cells employ Molecular Motors. The motors operate by transporting cargoes along the so-called cellular micro-tubules, namely rope-like structures that connect, for instance, the cell-nucleus and outer membrane. We introduce a new Markov Chain, the killed Quasi-Random-Walk, for such transport molecules and derive properties like the maximal run length and time. Furthermore we introduce permuted balance, which is a more flexible extension of the ordinary reversibility and introduce the notion of Time Duality, which compares certain passage times pathwise. We give a number of sufficient conditions for Time Duality based on the geometry of the transition graph. Both notions are closely related to properties of the killed Quasi-Random-Walk.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2 (2013) 1 
KW  - Markov chain
KW  - time duality
KW  - transition path theory
KW  - absorption
KW  - molecular motor
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-63045
ER  -