2019 | First order convergence of weak Wong–Zakai approximations of Lévy-driven Marcus SDEs | T. Kosenkova, A. Kulik, I. PavlyukevichZeitschrift: Theory Stoch. Process.Reihe: 24 (40)Seiten: 32-60Band: 2
First order convergence of weak Wong–Zakai approximations of Lévy-driven Marcus SDEs
Autoren: T. Kosenkova, A. Kulik, I. Pavlyukevich
(2019)
Zeitschrift:
Theory Stoch. Process.
2019 | Conditioned point processes with application to Lévy bridges | Giovanni Conforti, Tetiana Kosenkova, Sylvie RoellyZeitschrift: Journal of Theoretical ProbabilitySeiten: 2111-2134Band: 32Link zur Publikation
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Link zum Preprint
Conditioned point processes with application to Lévy bridges
Autoren: Giovanni Conforti, Tetiana Kosenkova, Sylvie Roelly
(2019)
Our first result concerns a characterisation by means of a functional equation of Poisson point processes conditioned by the value of their first moment. It leads to a generalised version of Mecke's formula. En passant, it also allows to gain quantitative results about stochastic domination for Poisson point processes under linear constraints.
Since bridges of a pure jump Lévy process in R^d with a height h can be interpreted as a Poisson point process on space-time conditioned by pinning its first moment to h, our approach allows us to characterize bridges of Lévy processes by means of a functional equation.
The latter result has two direct applications:
first we obtain a constructive and simple way to sample Lévy bridge dynamics; second it allows to estimate the number of jumps for such bridges. We finally show that our method remains valid for linearly perturbed Lévy processes like periodic Ornstein-Uhlenbeck processes driven by Lévy noise.
Zeitschrift:
Journal of Theoretical Probability
2017 | Transportation distances and noise sensitivity of multiplicative Lévy SDE with applications | Jan Gairing, Michael Högele, Tetiana KosenkovaZeitschrift: Stochastic Processes and their ApplicationsLink zur Publikation
Transportation distances and noise sensitivity of multiplicative Lévy SDE with applications
Autoren: Jan Gairing, Michael Högele, Tetiana Kosenkova
(2017)
Zeitschrift:
Stochastic Processes and their Applications
2017 | How close are time series to power tail Lévy diffusions? | Jan Gairing, Michael Hoegele, Tania Kosenkova, and Adam MonahanZeitschrift: Chaos: An Interdisciplinary Journal of Nonlinear SciencesBand: 27 (11) 073112-1--073112-20, DOI: 10.1063/1.4986496Link zur Publikation
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Link zum Preprint
How close are time series to power tail Lévy diffusions?
Autoren: Jan Gairing, Michael Hoegele, Tania Kosenkova, and Adam Monahan
(2017)
Zeitschrift:
Chaos: An Interdisciplinary Journal of Nonlinear Sciences
Band:
27 (11) 073112-1--073112-20, DOI: 10.1063/1.4986496
2016 | On the Calibration of Lévy Driven Time Series with Coupling Distances and an Application in Paleoclimate | J. Gairing, M. Högele, T. Kosenkova, A. KulikVerlag: SpringerBuchtitel: Mathematical Paradigms of Climate ScienceSeiten: 115-135Link zur Publikation
On the Calibration of Lévy Driven Time Series with Coupling Distances and an Application in Paleoclimate
Autoren: J. Gairing, M. Högele, T. Kosenkova, A. Kulik
(2016)
Buchtitel:
Mathematical Paradigms of Climate Science
2015 | Coupling distances between Lévy measures and applications to noise sensitivity of SDE | J. Gairing, M. Högele, T. Kosenkova, A. KulikZeitschrift: Stochastics and Dynamics 2 (2015)Link zur Publikation
Coupling distances between Lévy measures and applications to noise sensitivity of SDE
Autoren: J. Gairing, M. Högele, T. Kosenkova, A. Kulik
(2015)
Zeitschrift:
Stochastics and Dynamics 2 (2015)
2014 | Transportation distance between the Lévy measures and stochastic equations for Lévy-type processes | T. Kosenkova, A. KulikZeitschrift: Modern Stochastics: Theory and Applications No 1, Vol. 1, (2014)Link zur Publikation
Transportation distance between the Lévy measures and stochastic equations for Lévy-type processes
Autoren: T. Kosenkova, A. Kulik
(2014)
Zeitschrift:
Modern Stochastics: Theory and Applications No 1, Vol. 1, (2014)
2013 | Strong Markov approximation of Lévy processes and their generalizations in a scheme of series | T. KosenkovaZeitschrift: Theory of Probability and Mathematical Statistics 86 (2013)Link zur Publikation
Strong Markov approximation of Lévy processes and their generalizations in a scheme of series
Autoren: T. Kosenkova
(2013)
Zeitschrift:
Theory of Probability and Mathematical Statistics 86 (2013)
2012 | Weak convergence of the series scheme of Markov chains to the solution of Lévy driven SDE | T. KosenkovaZeitschrift: Theory of Stochastic Processes 18(34) 1 (2012)Link zur Publikation
Weak convergence of the series scheme of Markov chains to the solution of Lévy driven SDE
Autoren: T. Kosenkova
(2012)
Zeitschrift:
Theory of Stochastic Processes 18(34) 1 (2012)
