@unpublished{EcksteinWiemann2013,
  author    = {Eckstein, Lars and Wiemann, Dirk},
  title     = {Introduction},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-85457},
  year      = {2013},
  language  = {en}
}
@unpublished{FedchenkoTarkhanov2013,
  author    = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich},
  title     = {A Class of Toeplitz Operators in Several Variables},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-68932},
  year      = {2013},
  abstract  = {We introduce the concept of Toeplitz operator associated with the Laplace-Beltrami operator on a compact Riemannian manifold with boundary. We characterise those Toeplitz operators which are Fredholm, thus initiating the index theory.},
  language  = {en}
}
@unpublished{RoellyRuszel2013,
  author    = {Roelly, Sylvie and Ruszel, Wioletta M.},
  title     = {Propagation of Gibbsianness for infinite-dimensional diffusions with space-time interaction},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-69014},
  year      = {2013},
  abstract  = {We consider infinite-dimensional diffusions where the interaction between the coordinates has a finite extent both in space and time. In particular, it is not supposed to be smooth or Markov. The initial state of the system is Gibbs, given by a strong summable interaction. If the strongness of this initial interaction is lower than a suitable level, and if the dynamical interaction is bounded from above in a right way, we prove that the law of the diffusion at any time t is a Gibbs measure with absolutely summable interaction. The main tool is a cluster expansion in space uniformly in time of the Girsanov factor coming from the dynamics and exponential ergodicity of the free dynamics to an equilibrium product measure.},
  language  = {en}
}
@unpublished{GairingHoegeleKosenkovaetal.2013,
  author    = {Gairing, Jan and H{\"o}gele, Michael and Kosenkova, Tetiana and Kulik, Alexei Michajlovič},
  title     = {Coupling distances between L{\´e}vy measures and applications to noise sensitivity of SDE},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-68886},
  year      = {2013},
  abstract  = {We introduce the notion of coupling distances on the space of L{\´e}vy measures in order to quantify rates of convergence towards a limiting L{\´e}vy jump diffusion in terms of its characteristic triplet, in particular in terms of the tail of the L{\´e}vy measure. The main result yields an estimate of the Wasserstein-Kantorovich-Rubinstein distance on path space between two L{\´e}vy diffusions in terms of the couping distances. We want to apply this to obtain precise rates of convergence for Markov chain approximations and a statistical goodness-of-fit test for low-dimensional conceptual climate models with paleoclimatic data.},
  language  = {en}
}
@unpublished{CattiauxFradonKuliketal.2013,
  author    = {Cattiaux, Patrick and Fradon, Myriam and Kulik, Alexei Michajlovič and Roelly, Sylvie},
  title     = {Long time behavior of stochastic hard ball systems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-68388},
  year      = {2013},
  abstract  = {We study the long time behavior of a system of two or three Brownian hard balls living in the Euclidean space of dimension at least two, submitted to a mutual attraction and to elastic collisions.},
  language  = {en}
}
@unpublished{LyTarkhanov2013,
  author    = {Ly, Ibrahim and Tarkhanov, Nikolai Nikolaevich},
  title     = {Generalised Beltrami equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-67416},
  year      = {2013},
  abstract  = {We enlarge the class of Beltrami equations by developping a stability theory for the sheaf of solutions of an overdetermined elliptic system of first order homogeneous partial differential equations with constant coefficients in the Euclidean space.},
  language  = {en}
}
@unpublished{ShlapunovTarkhanov2013,
  author    = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {Sturm-Liouville problems in domains with non-smooth edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-67336},
  year      = {2013},
  abstract  = {We consider a (generally, non-coercive) mixed boundary value problem in a bounded domain for a second order elliptic differential operator A. The differential operator is assumed to be of divergent form and the boundary operator B is of Robin type. The boundary is assumed to be a Lipschitz surface. Besides, we distinguish a closed subset of the boundary and control the growth of solutions near this set. We prove that the pair (A,B) induces a Fredholm operator L in suitable weighted spaces of Sobolev type, the weight function being a power of the distance to the singular set. Moreover, we prove the completeness of root functions related to L.},
  language  = {en}
}
@unpublished{Wallenta2013,
  author    = {Wallenta, Daniel},
  title     = {A Lefschetz fixed point formula for elliptic quasicomplexes},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-67016},
  year      = {2013},
  abstract  = {In a recent paper with N. Tarkhanov, the Lefschetz number for endomorphisms (modulo trace class operators) of sequences of trace class curvature was introduced. We show that this is a well defined, canonical extension of the classical Lefschetz number and establish the homotopy invariance of this number. Moreover, we apply the results to show that the Lefschetz fixed point formula holds for geometric quasiendomorphisms of elliptic quasicomplexes.},
  language  = {en}
}
@unpublished{AlsaedyTarkhanov2013,
  author    = {Alsaedy, Ammar and Tarkhanov, Nikolai Nikolaevich},
  title     = {Normally solvable nonlinear boundary value problems},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-65077},
  year      = {2013},
  abstract  = {We study a boundary value problem for an overdetermined elliptic system of nonlinear first order differential equations with linear boundary operators. Such a problem is solvable for a small set of data, and so we pass to its variational formulation which consists in minimising the discrepancy. The Euler-Lagrange equations for the variational problem are far-reaching analogues of the classical Laplace equation. Within the framework of Euler-Lagrange equations we specify an operator on the boundary whose zero set consists precisely of those boundary data for which the initial problem is solvable. The construction of such operator has much in common with that of the familiar Dirichlet to Neumann operator. In the case of linear problems we establish complete results.},
  language  = {en}
}
@unpublished{HoegeleRuffino2013,
  author    = {H{\"o}gele, Michael and Ruffino, Paulo},
  title     = {Averaging along L{\´e}vy diffusions in foliated spaces},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-64926},
  year      = {2013},
  abstract  = {We consider an SDE driven by a L{\´e}vy noise on a foliated manifold, whose trajectories stay on compact leaves. We determine the effective behavior of the system subject to a small smooth transversal perturbation of positive order epsilon. More precisely, we show that the average of the transversal component of the SDE converges to the solution of a deterministic ODE, according to the average of the perturbing vector field with respect to the invariant measures on the leaves (of the unpertubed system) as epsilon goes to 0. In particular we give upper bounds for the rates of convergence. The main results which are proved for pure jump L{\´e}vy processes complement the result by Gargate and Ruffino for Stratonovich SDEs to L{\´e}vy driven SDEs of Marcus type.},
  language  = {en}
}