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Approximation and Stability of Solutions of SDEs Driven by a Symmetric α Stable Process with Non-Lipschitz Coefficients

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Séminaire de Probabilités XLV

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 2078))

Abstract

Firstly, we investigate Euler–Maruyama approximation for solutions of stochastic differential equations (SDEs) driven by a symmetric α stable process under Komatsu condition for coefficients. The approximation implies naturally the existence of strong solutions. Secondly, we study the stability of solutions under Komatsu condition, and also discuss it under Belfadli–Ouknine condition.

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Acknowledgements

This work is motivated by fruitful discussions with Toshio Yamada. The author would like to thank him very much. Professor Shinzo Watanabe reviewed original manuscript and offered some polite suggestions. The author also would like to thank him very much for his valuable comments. The author would like to express his thanks to the anonymous referee for several helpful corrections and suggestions.

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Authors and Affiliations

  1. Sanwa Kagaku Kenkyusho Co., Ltd., Nagoya, Japan

    Hiroya Hashimoto

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  1. Hiroya Hashimoto
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Correspondence to Hiroya Hashimoto .

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Editors and Affiliations

  1. , Laboratoire de Mathématiques, Université de Versailles-St Quentin, avenue des États-Unis 45, Versailles, 78035, France

    Catherine Donati-Martin

  2. IECN, Campus scientifique, BP 239, Nancy-Université, INRIA, Vandoeuvre-lès-Nancy, 54506, France

    Antoine Lejay

  3. Laboratoire de Mathématiques, Université de Versailles-St-Quentin, avenue des Etats-Unis 45, Versailles, 78035, France

    Alain Rouault

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Hashimoto, H. (2013). Approximation and Stability of Solutions of SDEs Driven by a Symmetric α Stable Process with Non-Lipschitz Coefficients. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLV. Lecture Notes in Mathematics(), vol 2078. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00321-4_7

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