Publications

2019 | Conditioned point processes with application to Lévy bridges | Giovanni Conforti, Tetiana Kosenkova, Sylvie RoellyZeitschrift: Journal of Theoretical ProbabilitySeiten: 2111-2134Band: 32Link zur Publikation , 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
Seiten:
2111-2134
Band:
32

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 , 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)

Verlag:
Springer
Buchtitel:
Mathematical Paradigms of Climate Science
Seiten:
115-135

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)