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A note on processes with random stationary increments
Affiliation:1. Department of Mathematics and Statistics, University of North Carolina at Greensboro, Greensboro, NC 27412, USA;2. Department of Statistics, Indiana University, Bloomington, IN 47408, USA;3. Department of Geography, Indiana University, Bloomington, IN 47408, USA;1. Mathematical Sciences Center and Tsinghua Center for Statistics Science, Tsinghua University, Beijing 100084, China;2. School of Economics and Wang Yanan Institute for Studies in Economics (WISE), Xiamen University, Xiamen 361005, China;3. School of Business, Renmin University of China, Beijing 100084, China;1. Afdeling Statistiek, Celestijnenlaan 200b - bus 2400, 3001 Leuven, Belgium;2. Faculty of Business and Economics, ORSTAT, KU Leuven, Belgium;1. University of Pittsburgh, United States;2. University of Haifa, Israel
Abstract:When the correlation theory is considered for the processes with random stationary increments, Yaglom (1955) has developed the spectral representation theory. In this note, we complete this development by obtaining the inversion formula of the spectrum in terms of the structure function.
Keywords:Intrinsic stationarity  Variogram  Spectrum  Structure function  Inversion formula
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