Conditional multidimensional random walks: Construction and limiting behaviour

• Antragsteller: Professor Dr. Vitali Wachtel
• Fachliche Zuordnung: Mathematik
• Förderung: Förderung von 2010 bis 2013
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 188691779

• Erstellungsjahr: 2014

Zusammenfassung der Projektergebnisse

For a long time exit times for random walks have been studied only via duality relations and corresponding factorisation identities. The main achievment of our project is a completely new approach to the study of exit times and corresponding conditioned distributions of Markov processes in discrete time. This method does not use duality, is quite robust and allows to obtain results for various models: multidimensional random walks in cones, integrated random walks and Markov chains with asymptotically zero drift.

Projektbezogene Publikationen (Auswahl)

• Random walks in cones. Ann. Probab.
  D. Denisov and V. Wachtel
  
• Exit times for integrated random walks. Ann. Inst. H. Poincare Probab. Statist.
  D. Denisov and V. Wachtel
  
• Martingale approach to subexponential asymptotics for random walks. Electron. Commun. Probab., 17(2012), Paper no, 6, 1-9
  D. Denisov and V. Wachtel
  (Siehe online unter https://doi.org/10.1214/ECP.v17-1757)
• Ordered random walks with heavy tails. Electron. J. Probab., 17(2012), Paper no, 5, 1-21
  D. Denisov and V. Wachtel
  
• Potential analysis for positive recurrent Markov chains with asymptotically zero drift: power-type asymptotics. Stochastic Process. Appl., 123(2013): 3027-3051
  D. Denisov, D. Korshunov and V. Wachtel
  (Siehe online unter https://doi.org/10.1016/j.spa.2013.04.011)
• Upper bounds for the maximum of a random walk with negative drift. J. Appl. Probab., 50(2013): 1131-1046
  J. Kugler and V. Wachtel
  
• Heavy traffic and heavy tails for subexponential distributions
  D. Denisov and J.Kugle
  
• Local limit theorem for the maximum of a random walk
  J. Kugler