@article{ConfortiRoelly2017,
  author    = {Conforti, Giovanni and Roelly, Sylvie},
  title     = {Bridge mixtures of random walks on an Abelian group},
  series = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability},
  volume    = {23},
  journal   = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability},
  publisher = {International Statistical Institute},
  address   = {Voorburg},
  issn      = {1350-7265},
  doi       = {10.3150/15-BEJ783},
  pages     = {1518 -- 1537},
  year      = {2017},
  language  = {en}
}
@article{CotroneiDiSalvoHolschneideretal.2017,
  author    = {Cotronei, Mariantonia and Di Salvo, Rosa and Holschneider, Matthias and Puccio, Luigia},
  title     = {Interpolation in reproducing kernel Hilbert spaces based on random subdivision schemes},
  series = {Journal of computational and applied mathematics},
  volume    = {311},
  journal   = {Journal of computational and applied mathematics},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0377-0427},
  doi       = {10.1016/j.cam.2016.08.002},
  pages     = {342 -- 353},
  year      = {2017},
  abstract  = {In this paper we present a Bayesian framework for interpolating data in a reproducing kernel Hilbert space associated with a random subdivision scheme, where not only approximations of the values of a function at some missing points can be obtained, but also uncertainty estimates for such predicted values. This random scheme generalizes the usual subdivision by taking into account, at each level, some uncertainty given in terms of suitably scaled noise sequences of i.i.d. Gaussian random variables with zero mean and given variance, and generating, in the limit, a Gaussian process whose correlation structure is characterized and used for computing realizations of the conditional posterior distribution. The hierarchical nature of the procedure may be exploited to reduce the computational cost compared to standard techniques in the case where many prediction points need to be considered.},
  language  = {en}
}
@article{DereudreMazzonettoRoelly2017,
  author    = {Dereudre, David and Mazzonetto, Sara and Roelly, Sylvie},
  title     = {Exact simulation of Brownian diffusions with drift admitting jumps},
  series = {SIAM journal on scientific computing},
  volume    = {39},
  journal   = {SIAM journal on scientific computing},
  number    = {3},
  publisher = {Society for Industrial and Applied Mathematics},
  address   = {Philadelphia},
  issn      = {1064-8275},
  doi       = {10.1137/16M107699X},
  pages     = {A711 -- A740},
  year      = {2017},
  abstract  = {In this paper, using an algorithm based on the retrospective rejection sampling scheme introduced in [A. Beskos, O. Papaspiliopoulos, and G. O. Roberts,Methodol. Comput. Appl. Probab., 10 (2008), pp. 85-104] and [P. Etore and M. Martinez, ESAIM Probab.Stat., 18 (2014), pp. 686-702], we propose an exact simulation of a Brownian di ff usion whose drift admits several jumps. We treat explicitly and extensively the case of two jumps, providing numerical simulations. Our main contribution is to manage the technical di ffi culty due to the presence of t w o jumps thanks to a new explicit expression of the transition density of the skew Brownian motion with two semipermeable barriers and a constant drift.},
  language  = {en}
}
@article{DereudreRoelly2017,
  author    = {Dereudre, David and Roelly, Sylvie},
  title     = {Path-dependent infinite-dimensional SDE with non-regular drift},
  series = {Annales de l'Institut Henri Poincar{\´e} : B, Probability and statistics},
  volume    = {53},
  journal   = {Annales de l'Institut Henri Poincar{\´e} : B, Probability and statistics},
  number    = {2},
  publisher = {Inst. of Mathematical Statistics},
  address   = {Bethesda},
  issn      = {0246-0203},
  doi       = {10.1214/15-AIHP728},
  pages     = {641 -- 657},
  year      = {2017},
  abstract  = {We establish in this paper the existence of weak solutions of infinite-dimensional shift invariant stochastic differential equations driven by a Brownian term. The drift function is very general, in the sense that it is supposed to be neither bounded or continuous, nor Markov. On the initial law we only assume that it admits a finite specific entropy and a finite second moment. The originality of our method leads in the use of the specific entropy as a tightness tool and in the description of such infinite-dimensional stochastic process as solution of a variational problem on the path space. Our result clearly improves previous ones obtained for free dynamics with bounded drift.},
  language  = {en}
}
@article{DimitrovaFernandesKoppitz2017,
  author    = {Dimitrova, Ilinka and Fernandes, Vitor H. and Koppitz, J{\"o}rg},
  title     = {A note on generators of the endomorphism semigroup of an infinite countable chain},
  series = {Journal of Algebra and its Applications},
  volume    = {16},
  journal   = {Journal of Algebra and its Applications},
  number    = {2},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {0219-4988},
  doi       = {10.1142/S0219498817500311},
  pages     = {9},
  year      = {2017},
  abstract  = {In this note, we consider the semigroup O(X) of all order endomorphisms of an infinite chain X and the subset J of O(X) of all transformations alpha such that vertical bar Im(alpha)vertical bar = vertical bar X vertical bar. For an infinite countable chain X, we give a necessary and sufficient condition on X for O(X) = < J > to hold. We also present a sufficient condition on X for O(X) = < J > to hold, for an arbitrary infinite chain X.},
  language  = {en}
}
@article{DimitrovaKoppitz2017,
  author    = {Dimitrova, Ilinka and Koppitz, J{\"o}rg},
  title     = {On the semigroup of all partial fence-preserving injections on a finite set},
  series = {Journal of Algebra and Its Applications},
  volume    = {16},
  journal   = {Journal of Algebra and Its Applications},
  number    = {12},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {0219-4988},
  doi       = {10.1142/S0219498817502231},
  pages     = {14},
  year      = {2017},
  abstract  = {For n∈N , let Xn={a1,a2,…,an} be an n-element set and let F=(Xn;<f) be a fence, also called a zigzag poset. As usual, we denote by In the symmetric inverse semigroup on Xn. We say that a transformation α∈In is fence-preserving if x<fy implies that xα<fyα, for all x,y in the domain of α. In this paper, we study the semigroup PFIn of all partial fence-preserving injections of Xn and its subsemigroup IFn={α∈PFIn:α-1∈PFIn}. Clearly, IFn is an inverse semigroup and contains all regular elements of PFIn. We characterize the Green's relations for the semigroup IFn. Further, we prove that the semigroup IFn is generated by its elements with rank ≥n-2. Moreover, for n∈2N, we find the least generating set and calculate the rank of IFn.},
  language  = {en}
}
@article{ElinShoikhetTarkhanov2017,
  author    = {Elin, Mark and Shoikhet, David and Tarkhanov, Nikolai Nikolaevich},
  title     = {Analytic Semigroups of Holomorphic Mappings and Composition Operators},
  series = {Computational Methods and Function Theory},
  volume    = {18},
  journal   = {Computational Methods and Function Theory},
  number    = {2},
  publisher = {Springer},
  address   = {Heidelberg},
  issn      = {1617-9447},
  doi       = {10.1007/s40315-017-0227-x},
  pages     = {269 -- 294},
  year      = {2017},
  abstract  = {In this manuscript we provide a review on the classical and resent results related to the problem of analytic extension in parameter for a semigroup of holomorphic self-mappings of the unit ball in a complex Banach space and its relation to the linear continuous semigroup of composition operators.},
  language  = {en}
}
@article{FedchenkoTarkhanov2017,
  author    = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich},
  title     = {A Rado theorem for the porous medium equation},
  series = {Boletin de la Sociedad Matem{\´a}tica Mexicana},
  volume    = {24},
  journal   = {Boletin de la Sociedad Matem{\´a}tica Mexicana},
  number    = {2},
  publisher = {Springer},
  address   = {Cham},
  issn      = {1405-213X},
  doi       = {10.1007/s40590-017-0169-3},
  pages     = {427 -- 437},
  year      = {2017},
  abstract  = {We prove that if u is a locally Lipschitz continuous function on an open set chi subset of Rn + 1 satisfying the nonlinear heat equation partial derivative(t)u = Delta(vertical bar u vertical bar(p-1) u), p > 1, weakly away from the zero set u(-1) (0) in chi, then u is a weak solution to this equation in all of chi.},
  language  = {en}
}
@article{GairingHoegeleKosenkova2017,
  author    = {Gairing, Jan and H{\"o}gele, Michael and Kosenkova, Tetiana},
  title     = {Transportation distances and noise sensitivity of multiplicative Levy SDE with applications},
  series = {Stochastic processes and their application},
  volume    = {128},
  journal   = {Stochastic processes and their application},
  number    = {7},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0304-4149},
  doi       = {10.1016/j.spa.2017.09.003},
  pages     = {2153 -- 2178},
  year      = {2017},
  abstract  = {This article assesses the distance between the laws of stochastic differential equations with multiplicative Levy noise on path space in terms of their characteristics. The notion of transportation distance on the set of Levy kernels introduced by Kosenkova and Kulik yields a natural and statistically tractable upper bound on the noise sensitivity. This extends recent results for the additive case in terms of coupling distances to the multiplicative case. The strength of this notion is shown in a statistical implementation for simulations and the example of a benchmark time series in paleoclimate.},
  language  = {en}
}
@article{GairingHogeleKosenkovaetal.2017,
  author    = {Gairing, Jan M. and Hogele, Michael A. and Kosenkova, Tania and Monahan, Adam H.},
  title     = {How close are time series to power tail Levy diffusions?},
  series = {Chaos : an interdisciplinary journal of nonlinear science},
  volume    = {27},
  journal   = {Chaos : an interdisciplinary journal of nonlinear science},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {1054-1500},
  doi       = {10.1063/1.4986496},
  pages     = {20},
  year      = {2017},
  abstract  = {This article presents a new and easily implementable method to quantify the so-called coupling distance between the law of a time series and the law of a differential equation driven by Markovian additive jump noise with heavy-tailed jumps, such as a-stable Levy flights. Coupling distances measure the proximity of the empirical law of the tails of the jump increments and a given power law distribution. In particular, they yield an upper bound for the distance of the respective laws on path space. We prove rates of convergence comparable to the rates of the central limit theorem which are confirmed by numerical simulations. Our method applied to a paleoclimate time series of glacial climate variability confirms its heavy tail behavior. In addition, this approach gives evidence for heavy tails in datasets of precipitable water vapor of the Western Tropical Pacific. Published by AIP Publishing.},
  language  = {en}
}