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Stochastic equations on compact groups in discrete negative time
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  • Published: 23 May 2007

Stochastic equations on compact groups in discrete negative time

  • Jirô Akahori1,
  • Chihiro Uenishi2 &
  • Kouji Yano3 

Probability Theory and Related Fields volume 140, pages 569–593 (2008)Cite this article

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Abstract

In this paper a stochastic equation on compact groups in discrete negative time is studied. The diagonal group action on the extreme points of solutions is proved to be transitive by means of the coupling method. This result is applied to generalize Yor’s work which is closely related to Tsirelson’s stochastic differential equation and to give criteria for existence of a strong solution and for uniqueness in law.

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Author information

Authors and Affiliations

  1. Ritsumeikan University, 1-1-1 Noji-higashi, Kusatsu, Shiga, 525-8577, Japan

    Jirô Akahori

  2. Cadem Corporation, Ltd., Shin-Yokohama Office, Houei-Shin-Yokohama Bldg., 2-14-9, Shin-Yokohama, Kouhoku-Ku, Yokohama, 222-0033, Japan

    Chihiro Uenishi

  3. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan

    Kouji Yano

Authors
  1. Jirô Akahori
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  2. Chihiro Uenishi
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  3. Kouji Yano
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Corresponding author

Correspondence to Kouji Yano.

Additional information

Dedicated to Professor Shinzo Watanabe on the occasion of his 70th birthday and to Professor Yoichiro Takahashi on the occasion of his 60th birthday.

This research was supported by Open Research Center Project for Private Universities: matching fund subsidy from MEXT, 2004–2008.

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Akahori, J., Uenishi, C. & Yano, K. Stochastic equations on compact groups in discrete negative time. Probab. Theory Relat. Fields 140, 569–593 (2008). https://doi.org/10.1007/s00440-007-0076-z

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  • Received: 24 July 2006

  • Revised: 14 March 2007

  • Published: 23 May 2007

  • Issue Date: March 2008

  • DOI: https://doi.org/10.1007/s00440-007-0076-z

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Keywords

  • Stochastic equation
  • Markov chain
  • Extreme points
  • Tannaka duality

Mathematics Subject Classification (2000)

  • 60H10
  • 60J05
  • 60B15
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