TY - INPR A1 - Keller, Peter A1 - Roelly, Sylvie A1 - Valleriani, Angelo T1 - A quasi-random-walk to model a biological transport process N2 - Transport Molecules play a crucial role for cell viability. Amongst others, linear motors transport cargos along rope-like structures from one location of the cell to another in a stochastic fashion. Thereby each step of the motor, either forwards or backwards, bridges a fixed distance. While moving along the rope the motor can also detach and is lost. We give here a mathematical formalization of such dynamics as a random process which is an extension of Random Walks, to which we add an absorbing state to model the detachment of the motor from the rope. We derive particular properties of such processes that have not been available before. Our results include description of the maximal distance reached from the starting point and the position from which detachment takes place. Finally, we apply our theoretical results to a concrete established model of the transport molecule Kinesin V. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 2 (2013) 3 KW - Markov chain KW - random walk KW - molecular motor KW - step process Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-63582 ER - TY - INPR A1 - Keller, Peter A1 - Roelly, Sylvie A1 - Valleriani, Angelo T1 - On time duality for quasi-birth-and-death processes N2 - We say that (weak/strong) time duality holds for continuous time quasi-birth-and-death-processes if, starting from a fixed level, the first hitting time of the next upper level and the first hitting time of the next lower level have the same distribution. We present here a criterion for time duality in the case where transitions from one level to another have to pass through a given single state, the so-called bottleneck property. We also prove that a weaker form of reversibility called balanced under permutation is sufficient for the time duality to hold. We then discuss the general case. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1 (2012) 4 KW - continuous time Markov chain KW - hitting times KW - time duality KW - absorbing boundary Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-56973 ER - TY - CHAP A1 - Valleriani, Angelo A1 - Roelly, Sylvie A1 - Kulik, Alexei Michajlovič ED - Roelly, Sylvie ED - Högele, Michael ED - Rafler, Mathias T1 - Stochastic processes with applications in the natural sciences BT - international workshop at Universidad de los Andes, Bogotá, Colombia T2 - Lectures in pure and applied mathematics N2 - The interdisciplinary workshop STOCHASTIC PROCESSES WITH APPLICATIONS IN THE NATURAL SCIENCES was held in Bogotá, at Universidad de los Andes from December 5 to December 9, 2016. It brought together researchers from Colombia, Germany, France, Italy, Ukraine, who communicated recent progress in the mathematical research related to stochastic processes with application in biophysics. The present volume collects three of the four courses held at this meeting by Angelo Valleriani, Sylvie Rœlly and Alexei Kulik. A particular aim of this collection is to inspire young scientists in setting up research goals within the wide scope of fields represented in this volume. Angelo Valleriani, PhD in high energy physics, is group leader of the team "Stochastic processes in complex and biological systems" from the Max-Planck-Institute of Colloids and Interfaces, Potsdam. Sylvie Rœlly, Docteur en Mathématiques, is the head of the chair of Probability at the University of Potsdam. Alexei Kulik, Doctor of Sciences, is a Leading researcher at the Institute of Mathematics of Ukrainian National Academy of Sciences. T3 - Lectures in pure and applied mathematics - 4 KW - macromolecular decay KW - Markov processes KW - branching processes KW - long-time behaviour KW - makromolekularer Zerfall KW - Markovprozesse KW - Verzweigungsprozesse KW - Langzeitverhalten Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-401802 SN - 978-3-86956-414-2 SN - 2199-4951 SN - 2199-496X IS - 4 PB - Universitätsverlag Potsdam CY - Potsdam ER -