@unpublished{Keller2009,
  author    = {Keller, Peter},
  title     = {Erzeugung gleichverteilter Stichproben von Lozenge-Teilungen mittels Kopplung von Markovketten},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49506},
  year      = {2009},
  abstract  = {Aus dem Inhalt: 1 Einleitung 2 Eigenschaften der Lozengeteilungen 3 Coupling From The Past (CFTP) 4 Simulation von uniform verteilten Lozengeteilungen 5 Programmlisting und Diskussion der Implementierung 6 Ausblick A Anhang},
  language  = {de}
}
@unpublished{KellerRoellyValleriani2013,
  author    = {Keller, Peter and Roelly, Sylvie and Valleriani, Angelo},
  title     = {A quasi-random-walk to model a biological transport process},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-63582},
  year      = {2013},
  abstract  = {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.},
  language  = {en}
}
@unpublished{KellerRoellyValleriani2012,
  author    = {Keller, Peter and Roelly, Sylvie and Valleriani, Angelo},
  title     = {On time duality for quasi-birth-and-death processes},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-56973},
  year      = {2012},
  abstract  = {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.},
  language  = {en}
}