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A study of a class of stochastic differential equations with non-Lipschitzian coefficients
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  • Published: 10 February 2005

A study of a class of stochastic differential equations with non-Lipschitzian coefficients

  • Shizan Fang1 &
  • Tusheng Zhang2 

Probability Theory and Related Fields volume 132, pages 356–390 (2005)Cite this article

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Abstract.

We study a class of stochastic differential equations with non-Lipschitz coefficients. A unique strong solution is obtained and the non confluence of the solutions of stochastic differential equations is proved. The dependence with respect to the initial values is investigated. To obtain a continuous version of solutions, the modulus of continuity of coefficients is assumed to be less than |x-y| log Finally a large deviation principle of Freidlin-Wentzell type is also established in the paper.

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Author information

Authors and Affiliations

  1. I.M.B, UFR Sciences et techniques, Université de Bourgogne, 9 avenue Alain Savary, B.P. 47870, 21078, Dijon, France

    Shizan Fang

  2. Department of Mathematics, University of Manchester, Oxford road, Manchester, M13 9PL, United Kingdom

    Tusheng Zhang

Authors
  1. Shizan Fang
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  2. Tusheng Zhang
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Fang, S., Zhang, T. A study of a class of stochastic differential equations with non-Lipschitzian coefficients. Probab. Theory Relat. Fields 132, 356–390 (2005). https://doi.org/10.1007/s00440-004-0398-z

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  • Received: 05 December 2003

  • Revised: 23 September 2004

  • Published: 10 February 2005

  • Issue Date: July 2005

  • DOI: https://doi.org/10.1007/s00440-004-0398-z

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Keywords

  • Gronwall lemma
  • Non-Lipschitz conditions
  • Pathwise uniqueness
  • Non-explosion
  • Non confluence
  • Large deviation principle
  • Euler approximation

Mathematics Subject Classification (2000)

  • 60H10
  • 60J60
  • 34A12
  • 34A40
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