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Large Deviations for Backward Stochastic Differential Equations Driven by G-Brownian Motion

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Abstract

In this paper, we consider forward–backward stochastic differential equation driven by G-Brownian motion (G-FBSDEs in short) with small parameter \(\varepsilon > 0\). We study the asymptotic behavior of the solution of the backward equation and establish a large deviation principle for the corresponding process.

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References

  1. Dembo, A., Zeitouni, O.: Large Deviations Techniques and Applications, 2nd edn. Springer, Berlin (1998)

    Book  Google Scholar 

  2. Denis, L., Hu, M., Peng, S.: Function spaces and capacity related to a sublinear expectation: application to \(G\)-brownian motion paths. Potential Anal. 34, 139–161 (2011)

    Article  MathSciNet  Google Scholar 

  3. Deuschel, J.D., Stroock, D.W.: Large Deviations. Academic Press Inc., Boston (1989)

    MATH  Google Scholar 

  4. Essaky, E.H.: Large deviation principle for a backward stochastic differential equation with subdifferential operator. Comptes Rendus Math. 346, 75–78 (2008)

    Article  MathSciNet  Google Scholar 

  5. Freidlin, M.I., Wentzell, A.D.: Random Perturbations of Dynamical Systems. Springer, Berlin (1984)

    Book  Google Scholar 

  6. Gao, F.: Pathwise properties and homeomorphic flows for stochastic differential equations driven by \(G\)-brownian motion. Stoch. Process. Appl. 119, 3356–3382 (2009)

    Article  MathSciNet  Google Scholar 

  7. Gao, F., Jiang, H.: Large deviations for stochastic differential equations driven by \(G\)-brownian motion. Stoch. Process. Appl. 120, 2212–2240 (2010)

    Article  MathSciNet  Google Scholar 

  8. Hu, M., Ji, S., Peng, S., Song, Y.: Backward stochastic differential equations driven by \(G\)-brownian motion. Stoch. Process. Appl. 124, 759–784 (2014)

    Article  MathSciNet  Google Scholar 

  9. Hu, M., Ji, S., Peng, S., Song, Y.: Comparison theorem, Feynman–Kac formula and Girsanov transformation for BSDEs driven by \(G\)-brownian motion. Stoch. Process. Appl. 124, 1170–1195 (2014)

    Article  MathSciNet  Google Scholar 

  10. Hu, M., Peng, S.: On representation theorem of \(G\)-expectations and paths of \(G\)-Brownian motion. Acta Mathe. Appl. Sin. Engl. Ser. 25, 539–546 (2009)

    Article  MathSciNet  Google Scholar 

  11. N’zi, M., Dakaou, I.: Large deviation for multivalued backward stochastic differential equations. Random Oper. Stoch. Equ. 22(2), 119–127 (2014)

    MathSciNet  MATH  Google Scholar 

  12. Peng, S.: Nonlinear expectations and stochastic calculus under uncertainty. arXiv:1002.4546v1 [math.PR] (2010)

  13. Rainero, S.: Un principe de grandes déviations pour une équation différentielle stochastique progressive rétrograde. C. R. Acad. Sci. Paris 343, 141–144 (2006)

    Article  MathSciNet  Google Scholar 

  14. Song, Y.: Some properties on \(G\)-evaluation and its applications to \(G\)-martingale decomposition. Sci. China Math. 54(2), 287–300 (2011)

    Article  MathSciNet  Google Scholar 

  15. Varadhan, S.R.S.: Large Deviations and Applications. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (1984)

    Book  Google Scholar 

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Acknowledgements

The authors would like to thank the anonymous referee and the AE for their helpful comments and suggestions that greatly improved the paper.

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Correspondence to Ibrahim Dakaou.

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Dakaou, I., Hima, A.S. Large Deviations for Backward Stochastic Differential Equations Driven by G-Brownian Motion. J Theor Probab 34, 499–521 (2021). https://doi.org/10.1007/s10959-020-01005-0

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  • DOI: https://doi.org/10.1007/s10959-020-01005-0

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