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Tsirel'son's equation in discrete time
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  • Published: June 1992

Tsirel'son's equation in discrete time

  • Mare Yor1 

Probability Theory and Related Fields volume 91, pages 135–152 (1992)Cite this article

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Summary

Motivated by Tsirel'son's equation in continuous time, a similar stochastic equation indexed by discrete negative time is discussed in full generality, in terms of the law of a discrete time noise. When uniqueness in law holds, the unique solution (in law) is not strong; moreover, when there exists a strong solution, there are several strong solution. In general, for any time,n, the σ-field generated by the past of a solution up to timen is shown to be equal, up to negligible sets, to the σ-field generated by the 3 following components: the infinitely remote past of the solution, the past to the noise up to timen, together with an adequate independent complement.

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Authors and Affiliations

  1. Laboratoire de Probabilités, Université Paris VI, 4, place Jussieu, Tour 56-3ème étage, F-75252, Paris Cedex 05, France

    Mare Yor

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  1. Mare Yor
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Yor, M. Tsirel'son's equation in discrete time. Probab. Th. Rel. Fields 91, 135–152 (1992). https://doi.org/10.1007/BF01291422

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  • Received: 03 April 1991

  • Revised: 25 July 1991

  • Issue Date: June 1992

  • DOI: https://doi.org/10.1007/BF01291422

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