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Extremal solutions for stochastic equations indexed by negative integers and taking values in compact groups

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  • Hirayama, Takao
  • Yano, Kouji

Abstract

Stochastic equations indexed by negative integers and taking values in compact groups are studied. Extremal solutions of the equations are characterized in terms of infinite products of independent random variables. This result is applied to characterize several properties of the set of all solutions in terms of the law of the driving noise.

Suggested Citation

  • Hirayama, Takao & Yano, Kouji, 2010. "Extremal solutions for stochastic equations indexed by negative integers and taking values in compact groups," Stochastic Processes and their Applications, Elsevier, vol. 120(8), pages 1404-1423, August.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:8:p:1404-1423
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    Citations

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    Cited by:

    1. C. R. E. Raja, 2015. "Operator Decomposable Measures and Stochastic Difference Equations," Journal of Theoretical Probability, Springer, vol. 28(3), pages 785-803, September.
    2. Hirayama, Takao & Yano, Kouji, 2013. "Strong solutions of Tsirel’son’s equation in discrete time taking values in compact spaces with semigroup action," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 824-828.
    3. Yu Ito & Toru Sera & Kouji Yano, 2023. "Resolution of Sigma-Fields for Multiparticle Finite-State Action Evolutions with Infinite Past," Journal of Theoretical Probability, Springer, vol. 36(3), pages 1368-1399, September.
    4. Kouji Yano, 2013. "Random Walk in a Finite Directed Graph Subject to a Road Coloring," Journal of Theoretical Probability, Springer, vol. 26(1), pages 259-283, March.

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