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Previsible sets for hyperfinite filtrations
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  • Published: September 1986

Previsible sets for hyperfinite filtrations

  • K. D. Stroyan1 

Probability Theory and Related Fields volume 73, pages 183–195 (1986)Cite this article

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Summary

Previsible (or predictable) stochastic processes are defined for any “filtration” over a probability space (Dellacherie and Meyer (1978), IV. 61). This technical definition gives previsible processes certain “predictability properties” such as not being able to oscillate in unison with martingale differentials. Thus previsibility has become one essential ingredient in “The General Theory of Stochastic Processes”.

We show that previsible sets for Keisler's (1984) special hyperfinite filtration are given both combinatorially and by a left filtration. Keisler's scheme has many other interesting features.

Our main technical tool is an extension of Henson's (1979) analysis of analytic sets and the standard part map.

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Authors and Affiliations

  1. Department of Mathematics, The University of Iowa, 52242, Iowa City, IA, USA

    K. D. Stroyan

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  1. K. D. Stroyan
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Cite this article

Stroyan, K.D. Previsible sets for hyperfinite filtrations. Probab. Th. Rel. Fields 73, 183–195 (1986). https://doi.org/10.1007/BF00339935

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  • Received: 15 July 1984

  • Revised: 22 January 1986

  • Issue Date: September 1986

  • DOI: https://doi.org/10.1007/BF00339935

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Keywords

  • Filtration
  • Stochastic Process
  • General Theory
  • Probability Theory
  • Statistical Theory
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