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Stochastic analysis on extended sample space and a tightness results
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  • Published: December 1990

Stochastic analysis on extended sample space and a tightness results

  • Zhen Qing Chen1 

Probability Theory and Related Fields volume 86, pages 517–549 (1990)Cite this article

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Summary

Approximate Markov process defined on the extended sample space plays an important role in the theory of Dirichlet Space. In this paper, stochastic analysis is studied on the extended sample space including the Stratonovitch integral, Ito's formula, etc. and a tightness and continuity results about excursion laws of the processes associated to a sequence of Dirichlet spaces is obtained by following an idea of Lyons and Zheng. These results are applied back to the standard sample space, which improve a few results about the additive functionals and also enable us to obtain the Lyons and Zheng's tightness and continuity results in the situation where the processes may blow up and have killings. Connections between the Stratonovitch integrals on the extended sample space and that defined by Nakao with respect to a function in the Dirichlet space is made.

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References

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Authors and Affiliations

  1. Department of Mathematics, Washington University, 63130, St. Louis, MO, USA

    Zhen Qing Chen

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  1. Zhen Qing Chen
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Cite this article

Chen, Z.Q. Stochastic analysis on extended sample space and a tightness results. Probab. Th. Rel. Fields 86, 517–549 (1990). https://doi.org/10.1007/BF01198173

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  • Received: 26 May 1989

  • Revised: 02 March 1990

  • Issue Date: December 1990

  • DOI: https://doi.org/10.1007/BF01198173

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Keywords

  • Stochastic Process
  • Probability Theory
  • Markov Process
  • Mathematical Biology
  • Standard Sample
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