ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 20, 43, 60 Singh, Ajit Iqbal, University of Delhi, India/Visiting: Institute of Biomathematics and Biometry, GSF Neuherberg, Germany, Lasser, Rupert, Institute of Biomathematics and Biometry, GSF Neuherberg and TU München, Germany Hypergroup-based stationarity properties of stochastic processes Let K be a hypergroup. R. Lasser and M. Leitner (J. Theoretical Probability, 1989) defined and studied K-weakly stationary processes, common estimates for the mean of a stationary process being the motivating example. J. C. Hardin and A. G. Miamee defined correlation autoregressive processes as another variant of the stationarity with applications to helicopter noise. We find sets of necessary conditions and of sufficient conditions for estimates of stationary processes with moving centres and oscillating lengths to be Kweakly stationary. We also determine when certain K-weakly stationary processes are correlation autoregressive, in particular for those related to Tchebychev polynomials and Dunkl–Ramirez’ example arising from p-adic numbers.