@unpublished{CattiauxFradonKuliketal.2013,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@unpublished{GairingHoegeleKosenkovaetal.2013,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}
}
@article{GairingHoegeleKosenkovaetal.2015,
  author    = {Gairing, Jan and H{\"o}gele, Michael and Kosenkova, Tetiana and Kulik, Alexei Michajlovič},
  title     = {Coupling distances between Levy measures and applications to noise sensitivity of SDE},
  series = {Stochastics and dynamic},
  volume    = {15},
  journal   = {Stochastics and dynamic},
  number    = {2},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {0219-4937},
  doi       = {10.1142/S0219493715500094},
  pages     = {25},
  year      = {2015},
  abstract  = {We introduce the notion of coupling distances on the space of Levy measures in order to quantify rates of convergence towards a limiting Levy jump diffusion in terms of its characteristic triplet, in particular in terms of the tail of the Levy measure. The main result yields an estimate of the Wasserstein-Kantorovich-Rubinstein distance on path space between two Levy diffusions in terms of the coupling 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{GairingHoegeleKosenkovaetal.2014,
  author    = {Gairing, Jan and H{\"o}gele, Michael and Kosenkova, Tetiana and Kulik, Alexei Michajlovič},
  title     = {On the calibration of L{\´e}vy driven time series with coupling distances : an application in paleoclimate},
  volume    = {3},
  number    = {2},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-69781},
  pages     = {18},
  year      = {2014},
  abstract  = {This article aims at the statistical assessment of time series with large fluctuations in short time, which are assumed to stem from a continuous process perturbed by a L{\´e}vy process exhibiting a heavy tail behavior. We propose an easily implementable procedure to estimate efficiently the statistical difference between the noisy behavior of the data and a given reference jump measure in terms of so-called coupling distances. After a short introduction to L{\´e}vy processes and coupling distances we recall basic statistical approximation results and derive rates of convergence. In the sequel the procedure is elaborated in detail in an abstract setting and eventually applied in a case study to simulated and paleoclimate data. It indicates the dominant presence of a non-stable heavy-tailed jump L{\´e}vy component for some tail index greater than 2.},
  language  = {en}
}
@book{Kulik2015,
  author    = {Kulik, Alexei Michajlovič},
  title     = {Introduction to Ergodic rates for Markov chains and processes},
  editor    = {Roelly, Sylvie},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  isbn      = {978-3-86956-338-1},
  issn      = {2199-4951},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-79360},
  publisher      = {Universit{\"a}t Potsdam},
  pages     = {ix, 122 S.},
  year      = {2015},
  abstract  = {The present lecture notes aim for an introduction to the ergodic behaviour of Markov Processes and addresses graduate students, post-graduate students and interested readers. Different tools and methods for the study of upper bounds on uniform and weak ergodic rates of Markov Processes are introduced. These techniques are then applied to study limit theorems for functionals of Markov processes. This lecture course originates in two mini courses held at University of Potsdam, Technical University of Berlin and Humboldt University in spring 2013 and Ritsumameikan University in summer 2013. Alexei Kulik, Doctor of Sciences, is a Leading researcher at the Institute of Mathematics of Ukrainian National Academy of Sciences.},
  language  = {en}
}
@inproceedings{VallerianiRoellyKulik2017,
  author    = {Valleriani, Angelo and Roelly, Sylvie and Kulik, Alexei Michajlovič},
  title     = {Stochastic processes with applications in the natural sciences},
  series = {Lectures in pure and applied mathematics},
  booktitle = {Lectures in pure and applied mathematics},
  number    = {4},
  editor    = {Roelly, Sylvie and H{\"o}gele, Michael and Rafler, Mathias},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  isbn      = {978-3-86956-414-2},
  issn      = {2199-4951},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-401802},
  pages     = {ix, 124},
  year      = {2017},
  abstract  = {The interdisciplinary workshop STOCHASTIC PROCESSES WITH APPLICATIONS IN THE NATURAL SCIENCES was held in Bogot{\´a}, at Universidad de los Andes from December 5 to December 9, 2016. It brought together researchers from Colombia, Germany, France, Italy, Ukraine, who communicated recent progress in the mathematical research related to stochastic processes with application in biophysics. The present volume collects three of the four courses held at this meeting by Angelo Valleriani, Sylvie Rœlly and Alexei Kulik. A particular aim of this collection is to inspire young scientists in setting up research goals within the wide scope of fields represented in this volume. Angelo Valleriani, PhD in high energy physics, is group leader of the team "Stochastic processes in complex and biological systems" from the Max-Planck-Institute of Colloids and Interfaces, Potsdam. Sylvie Rœlly, Docteur en Math{\´e}matiques, is the head of the chair of Probability at the University of Potsdam. Alexei Kulik, Doctor of Sciences, is a Leading researcher at the Institute of Mathematics of Ukrainian National Academy of Sciences.},
  language  = {en}
}