@article{ConfortiKosenkovaRoelly2019,
  author    = {Conforti, Giovanni and Kosenkova, Tetiana and Roelly, Sylvie},
  title     = {Conditioned Point Processes with Application to Levy Bridges},
  series = {Journal of theoretical probability},
  volume    = {32},
  journal   = {Journal of theoretical probability},
  number    = {4},
  publisher = {Springer},
  address   = {New York},
  issn      = {0894-9840},
  doi       = {10.1007/s10959-018-0863-8},
  pages     = {2111 -- 2134},
  year      = {2019},
  abstract  = {Our first result concerns a characterization by means of a functional equation of Poisson point processes conditioned by the value of their first moment. It leads to a generalized version of Mecke's formula. En passant, it also allows us to gain quantitative results about stochastic domination for Poisson point processes under linear constraints. Since bridges of a pure jump L{\´e}vy process in Rd with a height a can be interpreted as a Poisson point process on space-time conditioned by pinning its first moment to a, our approach allows us to characterize bridges of L{\´e}vy processes by means of a functional equation. The latter result has two direct applications: First, we obtain a constructive and simple way to sample L{\´e}vy bridge dynamics; second, it allows us to estimate the number of jumps for such bridges. We finally show that our method remains valid for linearly perturbed L{\´e}vy processes like periodic Ornstein-Uhlenbeck processes driven by L{\´e}vy noise.},
  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}
}
@unpublished{GairingHoegeleKosenkova2016,
  author    = {Gairing, Jan and H{\"o}gele, Michael and Kosenkova, Tetiana},
  title     = {Transportation distances and noise sensitivity of multiplicative L{\´e}vy SDE with applications},
  volume    = {5},
  number    = {2},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-86693},
  pages     = {24},
  year      = {2016},
  abstract  = {This article assesses the distance between the laws of stochastic differential equations with multiplicative L{\´e}vy noise on path space in terms of their characteristics. The notion of transportation distance on the set of L{\´e}vy 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{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}
}
@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}
}