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Stability Problem for One-Dimensional Stochastic Differential Equations with Discontinuous Drift

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Séminaire de Probabilités XLVIII

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 2168))

Abstract

We consider one-dimensional stochastic differential equations (SDEs) with irregular coefficients. The goal of this paper is to estimate the L p(Ω)-difference between two SDEs using a norm associated to the difference of coefficients. In our setting, the (possibly) discontinuous drift coefficient satisfies a one-sided Lipschitz condition and the diffusion coefficient is bounded, uniformly elliptic and Hölder continuous. As an application of this result, we consider the stability problem for this class of SDEs.

2010 Mathematics Subject Classification: 58K25, 41A25, 65C30

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Acknowledgements

The author is very grateful to Professor Arturo Kohatsu-Higa for his supports and fruitful discussions. The author would also like to thank Hideyuki Tanaka and Takahiro Tsuchiya for their useful advices. The author would like to express my thanks to Professor Toshio Yamada for his encouragement and comments. The author also thanks the referees for their comments which helped to improve the paper.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu, Shiga, 525-8577, Japan

    Dai Taguchi

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  1. Dai Taguchi
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Correspondence to Dai Taguchi .

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Editors and Affiliations

  1. Laboratoire de Mathématiques, Université de Versailles-St Quentin, Versailles , France

    Catherine Donati-Martin

  2. Campus scientifique, IECL, Vandoeuvre-les-Nancy CEDEX, France

    Antoine Lejay

  3. Laboratoire de Mathématiques, Université de Versailles-St Quentin, Versailles, France

    Alain Rouault

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Taguchi, D. (2016). Stability Problem for One-Dimensional Stochastic Differential Equations with Discontinuous Drift. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLVIII. Lecture Notes in Mathematics(), vol 2168. Springer, Cham. https://doi.org/10.1007/978-3-319-44465-9_4

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