Spectral representation of intrinsically stationary fields |
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Authors: | Georg Berschneider |
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Institution: | Institut für Mathematische Stochastik, Technische Universität Dresden, 01062 Dresden, Germany |
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Abstract: | Transferring the concept of processes with weakly stationary increments to arbitrary locally compact Abelian groups two closely related notions arise: while intrinsically stationary random fields can be seen as a direct analog of intrinsic random functions of order k applied by G. Matheron in geostatistics, stationarizable random fields arise as a natural analog of definitizable functions in harmonic analysis. We concentrate on intrinsically stationary random fields related to finite-dimensional, translation-invariant function spaces, establish an orthogonal decomposition of random fields of this type, and present spectral representations for intrinsically stationary as well as stationarizable random fields using orthogonal vector measures. |
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Keywords: | 60G10 42A82 62M15 86A32 |
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