Forschung

DFG-Project: "Nichtlineare stochastische Fixpunktgleichungen mit Anwendungen in der Statistischen Mechanik" (seit 2017)

1. 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
2. Large excursions and conditioned laws for recursive sequences generated by random matrices
   joint work with Jeffrey Collamore
   Ann. Probab. 46, 2064-2120 (2018)  arxiv
   
3. 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
   
4. Solutions to Complex Smoothing Equations
   joint work with Matthias Meiners
   Probab. Theory Relat. Fields, 168(1-2), 199-268 (2017) springerlink arxiv
   
5. 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
   
6. 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
   
7. Fixed Points of the Multivariate Smoothing Transform
   Probab. Theory Rel. Fields 164(1), 401-458 (2016) arxiv springerlink
   
8. 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
   
9. On Kesten's Multivariate Choquet-Deny Lemma
   Electronic Communications in Probability 18(65), 1-7 (2013) arxiv ejpecp
10. 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
11. 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
    
12. 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
    
13. 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