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

Part of the Lecture Notes in Mathematics book series (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.

Keywords

  • Euler–Maruyama approximation
  • Stability of solution
  • Symmetric α stable process

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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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Correspondence to Hiroya Hashimoto .

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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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