@unpublished{LyTarkhanov2013,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@unpublished{Roelly2013,
  author    = {Roelly, Sylvie},
  title     = {Reciprocal processes : a stochastic analysis approach},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-64588},
  year      = {2013},
  abstract  = {Reciprocal processes, whose concept can be traced back to E. Schr{\"o}dinger, form a class of stochastic processes constructed as mixture of bridges, that satisfy a time Markov field property. We discuss here a new unifying approach to characterize several types of reciprocal processes via duality formulae on path spaces: The case of reciprocal processes with continuous paths associated to Brownian diffusions and the case of pure jump reciprocal processes associated to counting processes are treated. This presentation is based on joint works with M. Thieullen, R. Murr and C. L{\´e}onard.},
  language  = {en}
}
@unpublished{MeleardRoelly2013,
  author    = {M{\´e}l{\´e}ard, Sylvie and Roelly, Sylvie},
  title     = {Evolutive two-level population process and large population approximations},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-64604},
  year      = {2013},
  abstract  = {We are interested in modeling the Darwinian evolution of a population described by two levels of biological parameters: individuals characterized by an heritable phenotypic trait submitted to mutation and natural selection and cells in these individuals influencing their ability to consume resources and to reproduce. Our models are rooted in the microscopic description of a random (discrete) population of individuals characterized by one or several adaptive traits and cells characterized by their type. The population is modeled as a stochastic point process whose generator captures the probabilistic dynamics over continuous time of birth, mutation and death for individuals and birth and death for cells. The interaction between individuals (resp. between cells) is described by a competition between individual traits (resp. between cell types). We are looking for tractable large population approximations. By combining various scalings on population size, birth and death rates and mutation step, the single microscopic model is shown to lead to contrasting nonlinear macroscopic limits of different nature: deterministic approximations, in the form of ordinary, integro- or partial differential equations, or probabilistic ones, like stochastic partial differential equations or superprocesses.},
  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{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{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{Eckstein2013,
  author    = {Eckstein, Lars},
  title     = {Monk Lewis's Timour the Tartar, grand romantic orientalism and imperial melancholy},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-85503},
  pages     = {23},
  year      = {2013},
  language  = {en}
}
@unpublished{Eckstein2013,
  author    = {Eckstein, Lars},
  title     = {Politics of passion and the production of human illegality},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-85512},
  pages     = {20},
  year      = {2013},
  language  = {en}
}
@unpublished{Eckstein2013,
  author    = {Eckstein, Lars},
  title     = {Filming illegals},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-85491},
  pages     = {13},
  year      = {2013},
  language  = {en}
}
@unpublished{NehringPoghosyanZessin2013,
  author    = {Nehring, Benjamin and Poghosyan, Suren and Zessin, Hans},
  title     = {On the construction of point processes in statistical mechanics},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-64080},
  year      = {2013},
  abstract  = {By means of the cluster expansion method we show that a recent result of Poghosyan and Ueltschi (2009) combined with a result of Nehring (2012) yields a construction of point processes of classical statistical mechanics as well as processes related to the Ginibre Bose gas of Brownian loops and to the dissolution in R^d of Ginibre's Fermi-Dirac gas of such loops. The latter will be identified as a Gibbs perturbation of the ideal Fermi gas. On generalizing these considerations we will obtain the existence of a large class of Gibbs perturbations of the so-called KMM-processes as they were introduced by Nehring (2012). Moreover, it is shown that certain "limiting Gibbs processes" are Gibbs in the sense of Dobrushin, Lanford and Ruelle if the underlying potential is positive. And finally, Gibbs modifications of infinitely divisible point processes are shown to solve a new integration by parts formula if the underlying potential is positive.},
  language  = {en}
}
@unpublished{Keller2013,
  author    = {Keller, Peter},
  title     = {Mathematical modeling of molecular motors},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-63045},
  year      = {2013},
  abstract  = {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.},
  language  = {en}
}
@unpublished{MakhmudovTarkhanov2013,
  author    = {Makhmudov, Olimdjan and Tarkhanov, Nikolai Nikolaevich},
  title     = {An extremal problem related to analytic continuation},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-63634},
  year      = {2013},
  abstract  = {We show that the usual variational formulation of the problem of analytic continuation from an arc on the boundary of a plane domain does not lead to a relaxation of this overdetermined problem. To attain such a relaxation, we bound the domain of the functional, thus changing the Euler equations.},
  language  = {en}
}
@unpublished{LeonardRoellyZambrini2013,
  author    = {L{\´e}onard, Christian and Roelly, Sylvie and Zambrini, Jean-Claude},
  title     = {Temporal symmetry of some classes of stochastic processes},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-64599},
  year      = {2013},
  abstract  = {In this article we analyse the structure of Markov processes and reciprocal processes to underline their time symmetrical properties, and to compare them. Our originality consists in adopting a unifying approach of reciprocal processes, independently of special frameworks in which the theory was developped till now (diffusions, or pure jump processes). This leads to some new results, too.},
  language  = {en}
}
@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{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{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{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{BagderinaTarkhanov2013,
  author    = {Bagderina, Yulia Yu. and Tarkhanov, Nikolai Nikolaevich},
  title     = {Differential invariants of a class of Lagrangian systems with two degrees of freedom},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-63129},
  year      = {2013},
  abstract  = {We consider systems of Euler-Lagrange equations with two degrees of freedom and with Lagrangian being quadratic in velocities. For this class of equations the generic case of the equivalence problem is solved with respect to point transformations. Using Lie's infinitesimal method we construct a basis of differential invariants and invariant differentiation operators for such systems. We describe certain types of Lagrangian systems in terms of their invariants. The results are illustrated by several examples.},
  language  = {en}
}
@unpublished{KiselevTarkhanov2013,
  author    = {Kiselev, Oleg and Tarkhanov, Nikolai Nikolaevich},
  title     = {The capture of a particle into resonance at potential hole with dissipative perturbation},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-64725},
  year      = {2013},
  abstract  = {We study the capture of a particle into resonance at a potential hole with dissipative perturbation and periodic outside force. The measure of resonance solutions is evaluated. We also derive an asymptotic formula for the parameter range of those solutions which are captured into resonance.},
  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}
}
@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}
}