@article{GerlachGlueck2019,
  author    = {Gerlach, Moritz Reinhardt and Gl{\"u}ck, Jochen},
  title     = {Convergence of positive operator semigroups},
  series = {Transactions of the American Mathematical Society},
  volume    = {372},
  journal   = {Transactions of the American Mathematical Society},
  number    = {9},
  publisher = {American Mathematical Soc.},
  address   = {Providence},
  issn      = {0002-9947},
  doi       = {10.1090/tran/7836},
  pages     = {6603 -- 6627},
  year      = {2019},
  abstract  = {We present new conditions for semigroups of positive operators to converge strongly as time tends to infinity. Our proofs are based on a novel approach combining the well-known splitting theorem by Jacobs, de Leeuw, and Glicksberg with a purely algebraic result about positive group representations. Thus, we obtain convergence theorems not only for one-parameter semigroups but also for a much larger class of semigroup representations. Our results allow for a unified treatment of various theorems from the literature that, under technical assumptions, a bounded positive C-0-semigroup containing or dominating a kernel operator converges strongly as t ->infinity. We gain new insights into the structure theoretical background of those theorems and generalize them in several respects; especially we drop any kind of continuity or regularity assumption with respect to the time parameter.},
  language  = {en}
}
@article{deWiljesReichStannat2018,
  author    = {de Wiljes, Jana and Reich, Sebastian and Stannat, Wilhelm},
  title     = {Long-Time stability and accuracy of the ensemble Kalman-Bucy Filter for fully observed processes and small measurement noise},
  series = {SIAM Journal on Applied Dynamical Systems},
  volume    = {17},
  journal   = {SIAM Journal on Applied Dynamical Systems},
  number    = {2},
  publisher = {Society for Industrial and Applied Mathematics},
  address   = {Philadelphia},
  issn      = {1536-0040},
  doi       = {10.1137/17M1119056},
  pages     = {1152 -- 1181},
  year      = {2018},
  abstract  = {The ensemble Kalman filter has become a popular data assimilation technique in the geosciences. However, little is known theoretically about its long term stability and accuracy. In this paper, we investigate the behavior of an ensemble Kalman-Bucy filter applied to continuous-time filtering problems. We derive mean field limiting equations as the ensemble size goes to infinity as well as uniform-in-time accuracy and stability results for finite ensemble sizes. The later results require that the process is fully observed and that the measurement noise is small. We also demonstrate that our ensemble Kalman-Bucy filter is consistent with the classic Kalman-Bucy filter for linear systems and Gaussian processes. We finally verify our theoretical findings for the Lorenz-63 system.},
  language  = {en}
}
@unpublished{FangXu2005,
  author    = {Fang, Daoyuan and Xu, Jiang},
  title     = {Asymptotic behavior of solutions to multidimensional nonisentropic hydrodynamic model for semiconductors},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29767},
  year      = {2005},
  abstract  = {In this paper, a global existence result of smooth solutions to the multidimen- sional nonisentropic hydrodynamic model for semiconductors is proved, under the assumption that the initial data is a perturbation of the stationary solutions for the thermal equilibrium state. The resulting evolutionary solutions converge to the stationary solutions in time asymptotically exponentially fast.},
  language  = {en}
}