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Isotropic Gauss-Markov currents
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  • Published: June 1989

Isotropic Gauss-Markov currents

  • Eugene Wong1,2 &
  • Moshe Zakai1,2 

Probability Theory and Related Fields volume 82, pages 137–154 (1989)Cite this article

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  • 5 Citations

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Summary

A natural definition of the Markov property for multi-parameter random processes (random fields) is the following. Let {X t,t∈ℝN} be a multiparameter process. For any set D in ℝN let σ D denote the σ-field generated by {X t , t∈D}. The field {X t,t∈D} is said to be Markov (or Markov of degree 1 [6], or sharp Markov) if, for any bounded open set D with smooth boundary, σ D and σ D c are conditionally independent given σ δD . It has been known for some time that to find interesting examples of Markov processes under this definition; it is necessary to consider generalized random functions. In this paper we show that a natural framework for the Markov property of multiparameter processes is a class of generalized random differential forms (i.e., random currents). Our principal objective is to relate the Markovian nature of an isotropic gaussian current to its spectral properties.

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Author information

Authors and Affiliations

  1. College of Engineering, Dept. of Electrical Engineering and Computer Sciences, University of California, 94720, Berkeley, CA, USA

    Eugene Wong & Moshe Zakai

  2. Technion, Haifa, Israel

    Eugene Wong & Moshe Zakai

Authors
  1. Eugene Wong
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  2. Moshe Zakai
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Additional information

Work supported by the Army Research Office, Grant No. DAAG 29-85-K-0233

Work done while at the University of California at Berkeley

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Wong, E., Zakai, M. Isotropic Gauss-Markov currents. Probab. Th. Rel. Fields 82, 137–154 (1989). https://doi.org/10.1007/BF00340015

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  • Received: 15 February 1987

  • Issue Date: June 1989

  • DOI: https://doi.org/10.1007/BF00340015

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Keywords

  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Markov Process
  • Random Process
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