Arbeitsgebiete und Interessen

• Limit theorems for weakly dependent random variables with values in finite and infinite dimensional spaces and their applications: central limit theorems; laws of the iterated logarithms; almost sure invariance principles; strong laws of large numbers
  
• Random fields: limit theorems for mixing random fields with values in finite and infinite dimensional spaces; weakly dependence conditions for random fields
  
• Theory of U- statistics: Limit theorems for U- statistics from independent and weakly dependent observations
  
• Autoregressive processes: estimation of parameters of autoregressive processes; autoregressive processes with weakly dependent innovations; autoregressive processes in Banach spaces
  
• Bootstrap: bootstrap for U-statistics of weakly dependent observations
  
• Change point analysis
  
• GARCH models

Eine Auswahl meiner Publikationen

• Marcinkiewich –Zygmund strong laws for U-statistics of weakly dependent observations. Statistics and Probability Letters, 2009,v.79, No.19, 2028-2036 (coauthor: H.Dehling)
• Laws of the iterated logarithms and an almost sure invariance principle for mixing B-valued random variables and autoregressive processes.Lithuanian Mathematical Journal, 2009, v.49, No. 2, 203-215
• On the accuracy of Gaussian approximation of the distribution of sums of weakly dependent random variables with values in Rm and lp. Uzbek Mathematical Journal, 2006, N3, 52-67.(coauthor: Parpieva N.T.)
• The bounded law of the iterated logarithm for weakly dependent random variables with values in a type 2 Banach space. Theory of Probab.and its applications. 2005, 49, N3., 444-457
• Estimations of mean and covariance operator for Banach space valued autoregressive processes with dependent innovations. Statistical Inference for Stochastic Processes. 2005, v. 8, N2, 137-149. (coauthor: H.Dehling)
• Rate of convergence in the central limit theorem for weakly dependent random variables with values in lp and co spaces. Uzbek Mathematical Journal, 2004, N2, 101-111
• Almost sure invariance principles for U-statistics and von Mises functionals from weakly dependent observations. Theory of Probability and its Applications. 2003. vol.47, N4 , 814-817
• The law of the iterated logarithm for weakly dependent Hilbert space valued random variables. Siberian Mathematical journal. 2003, vol. 44, N.6, 1111-1126 .
• Strong limit theorems for mixing random variables with values in Hilbert space and their applications. Progress in Probability, 2003, vol. 55, 153-174. Birkhauser Verlag Basel/Switzerland.
• Poisson limits for U-statistics. Stochastic Processes and Their Applications, 2002, Vol. 99, 137-157. (coauthors: A. Dabrowski , H. Dehling, T.Mikosch )

Stipendien

• DFG (German Scientific Foundation) in 2008
• ICTP (The Abdus Salam International Centre for Theoretical Physics), Trieste, Italy in 2006
• DAAD (German Academic Exchange Service) in 2006
• DAAD (German Academic Exchange Service) in 2001
• The Committee of Science and Technology of the Republic of Uzbekistan in 1999

Forschungsbesuche

• Bochum University, Germany (09/2001-12/2001; 04/2003-07/2003; 10/2006-12/2006; 09/2008-12/2008; 09/2009-02/2010)
• Putra University, Malaysia (04/2009-06/2009)
• ICTP (International Centre for Theoretical Physics), Trieste, Italy (09/2007-12/2007)
• Groningen University, The Netherlands (12/1999-02/2001)

Gastvorträge

• Dresden Technology University,Germany, 2006
• Moscow State University, Russia, 2004
• Copenhagen University, Denmark 2001
• Kiel University, Germany, 2001
• Göttingen University, Germany, 2001
• Delft Technology University ,The Netherlands, 2000

Persönliches