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Spectral representation of intrinsically stationary fields

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  • Berschneider, Georg

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.

Suggested Citation

  • Berschneider, Georg, 2012. "Spectral representation of intrinsically stationary fields," Stochastic Processes and their Applications, Elsevier, vol. 122(12), pages 3837-3851.
  • Handle: RePEc:eee:spapps:v:122:y:2012:i:12:p:3837-3851 DOI: 10.1016/j.spa.2012.07.005
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    1. Rozkosz, Andrzej & Slominski, Leszek, 1997. "On stability and existence of solutions of SDEs with reflection at the boundary," Stochastic Processes and their Applications, Elsevier, vol. 68(2), pages 285-302, June.
    2. Ramasubramanian, S., 2006. "An insurance network: Nash equilibrium," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 374-390, April.
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