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Embedding and asymptotic expansions for martingales
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  • Published: December 1995

Embedding and asymptotic expansions for martingales

  • P. A. Mykland1 

Probability Theory and Related Fields volume 103, pages 475–492 (1995)Cite this article

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Summary

The paper develops a way of embedding general martingales in continuous ones in such a way that the quadratic variation of the continuous martingale has conditional cumulants (given the original martingale) that are explicitly given in terms of optional and predictable variations of the original process. Bartlett identities for the conditional cumulants are also found. A main corollary to these results is the establishment of second (and in some cases higher) order asymptotic expansions for martingales.

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Author information

Authors and Affiliations

  1. Department of Statistics, The University of Chicago, 60637, Chicago, IL, USA

    P. A. Mykland

Authors
  1. P. A. Mykland
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Additional information

Research supported in part by National Science Foundation grant DMS 93-05601 and Army Research Office grant DAAH04-1-0105

This manuscript was prepared using computer facilities supported in part by the National Science Foundation grants DMS 89-05292, DMS 87-03942, and DMS 86-01732 awarded to the Department of Statistics at The University of Chicago, and by The University of Chicago Block Fund

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Mykland, P.A. Embedding and asymptotic expansions for martingales. Probab. Th. Rel. Fields 103, 475–492 (1995). https://doi.org/10.1007/BF01246335

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  • Received: 20 June 1994

  • Revised: 17 April 1995

  • Issue Date: December 1995

  • DOI: https://doi.org/10.1007/BF01246335

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Mathematics Subject Classification (1991)

  • 60G42
  • 60G44
  • 60F99
  • 62E20
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