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Stochastic differential equations for multi-dimensional domain with reflecting boundary
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  • Published: September 1987

Stochastic differential equations for multi-dimensional domain with reflecting boundary

  • Yasumasa Saisho1 

Probability Theory and Related Fields volume 74, pages 455–477 (1987)Cite this article

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Summary

In this paper we prove that there exists a unique solution of the Skorohod equation for a domain inR d with a reflecting boundary condition. We remove the admissibility condition of the domain which is assumed in the work [4] of Lions and Sznitman. We first consider a deterministic case and then discuss a stochastic case.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Technology, Keio University, Yokohama, Japan

    Yasumasa Saisho

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  1. Yasumasa Saisho
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Saisho, Y. Stochastic differential equations for multi-dimensional domain with reflecting boundary. Probab. Th. Rel. Fields 74, 455–477 (1987). https://doi.org/10.1007/BF00699100

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  • Received: 14 June 1985

  • Issue Date: September 1987

  • DOI: https://doi.org/10.1007/BF00699100

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Keywords

  • Stochastic Differential Equation
  • Admissibility Condition
  • Uniform Continuity
  • Unique Strong Solution
  • Brownian Path
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