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An inequality for the semi-martingales application to stochastic differential equations

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Part of the Lecture Notes in Mathematics book series (LNM,volume 656)

Abstract

We prove the existence and unicity of a strong solution for the stochastic differential equation dXt=a(X,t)dt, where a is "predictable", locally bounded and locally lipschitzian and X is a semi-martingale (cf. [3]). The pro of uses an inequality for such a semi-martingale which is established in the paragraph B. There results have been shown in [2] and generalize [1].

Keywords

  • Banach Space
  • Stochastic Differential Equation
  • Strong Solution
  • Local Martingale
  • Finite Variation

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References

  1. C. Doleans-Dade: On the existence and unicity of stochastic integral equations.

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  2. M. Metivier et J. Pellaumail: Inégalites pour une martingale et équations différentielles stochastiques. Séminaire de Rennes 1977 (to appear).

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  3. P.A. Meyer: Séminaire de probabilités X, Springer-Verlag 1976.

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© 1978 Springer-Verlag

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Pellaumail, J. (1978). An inequality for the semi-martingales application to stochastic differential equations. In: Weron, A. (eds) Probability Theory on Vector Spaces. Lecture Notes in Mathematics, vol 656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0068820

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  • DOI: https://doi.org/10.1007/BFb0068820

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08846-2

  • Online ISBN: 978-3-540-35814-5

  • eBook Packages: Springer Book Archive