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Approximation and support theorems in modulus spaces
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  • Published: December 1995

Approximation and support theorems in modulus spaces

  • István Gyöngy1,
  • David Nualart2 &
  • Marta Sanz-Sole2 

Probability Theory and Related Fields volume 101, pages 495–509 (1995)Cite this article

  • 111 Accesses

  • 15 Citations

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Summary

We prove an approximation theorem for stochastic differential equations, under rather weak smoothness conditions on the coefficients, when the driving semimartingales are approximated by continuous semimartingales, in probability, and the solutions are considered in several Banach spaces, defined in terms of different types of the modulus of continuity. Hence Stroock-Varadhan's support theorem is obtained in these spaces, in particular, in appropriate Besov and Hölder spaces.

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Author information

Authors and Affiliations

  1. Department of Probability and Statistics, Eötvös University Budapest, Múzeum krt 6-8, H-1088, Budapest, Hungary

    István Gyöngy

  2. Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, E-08007, Barcelona, Spain

    David Nualart & Marta Sanz-Sole

Authors
  1. István Gyöngy
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  2. David Nualart
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  3. Marta Sanz-Sole
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Additional information

Partially supported by the Foundation of National Research n° 2290

Partially supported by the DGICYT grant no PB 90-0452

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Gyöngy, I., Nualart, D. & Sanz-Sole, M. Approximation and support theorems in modulus spaces. Probab. Th. Rel. Fields 101, 495–509 (1995). https://doi.org/10.1007/BF01202782

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  • Received: 14 March 1994

  • Revised: 20 September 1994

  • Issue Date: December 1995

  • DOI: https://doi.org/10.1007/BF01202782

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Mathematics Subject Classification

  • 60H10
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