Forschung
Forschung
- Non-Gaussian limit theorems
- Branching processes, in particular Multitype Branching Random Walks
- Extreme value theory, in particular for time series
- Heavy-tailed random variables
- Conditional limit theorems
DFG-Project: "Nichtlineare stochastische Fixpunktgleichungen mit Anwendungen in der Statistischen Mechanik" (seit 2017)
Publications
- Absolute Continuity of Complex Martingales and of Solutions to Complex Smoothing Equations
joint work with Ewa Damek
Electronic Communications in Probability 23(60), 1-12 (2018). arxiv ecp - Large excursions and conditioned laws for recursive sequences generated by random matrices
joint work with Jeffrey Collamore
Ann. Probab. 46, 2064-2120 (2018) arxiv
- Precise Tail Asymptotics for Attracting Fixed Points of Multivariate Smoothing Transformations
joint work with Dariusz Buraczewski
Markov Processes Relat. Fields 23, 147-170 (2017) arxiv
- Solutions to Complex Smoothing Equations
joint work with Matthias Meiners
Probab. Theory Relat. Fields, 168(1-2), 199-268 (2017) springerlink arxiv
- Fixed Points of the Multivariate Smoothing Transform: The Critical Case
joint work with Konrad Kolesko
Electronic Journal of Probability 20(52), 1-24 (2015) arxiv ejpecp
- Precise Large Deviation Results for Products of Random Matrices
joint work with Dariusz Buraczewski
Annales de l'Institut Henri Poincare Probab. Statist. 52(3), 1474-1513 (2016). arxiv projecteuclid
- Fixed Points of the Multivariate Smoothing Transform
Probab. Theory Rel. Fields 164(1), 401-458 (2016) arxiv springerlink
- On Multidimensional Mandelbrot Cascades
joint work with Dariusz Buraczewski, Ewa Damek and Yves Guivarc'h
J. Diff. Equation Appl. 20(11), 1523-1567 (2014) arxiv tandfonline
- On Kesten's Multivariate Choquet-Deny Lemma
Electronic Communications in Probability 18(65), 1-7 (2013) arxiv ejpecp - Heavy tailed solutions of multivariate smoothing transforms
joint work with Dariusz Buraczewski, Ewa Damek and Mariusz Mirek
Stochastic Processes and their Applications 123(6), 1947-1986 (2013) arxiv sciencedirect - Precise tail index of fixed points of the two-sided smoothing transform
joint work with Gerold Alsmeyer and Ewa Damek
Random Matrices and Iterated Random Functions. Springer Proceedings in Mathematics & Statistics, Vol. 53 arxiv springerlink
- Convergence to stable laws for multidimensional stochastic recursions: the case of regular matrices
joint work with Ewa Damek, Mariusz Mirek and Jacek Zienkiewicz
Potential Analysis 38(3), 683-697 (2013) arxiv springerlink
- Tail behavior of stationary solutions of random difference equations: the case of regular matrices
joint work with Gerold Alsmeyer
J. Diff. Equation Appl. 18(8), 1305-1332 (2012) arxiv tandfonline