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Large deviations and support theorem for diffusion processes via rough paths

Author

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  • Ledoux, M.
  • Qian, Z.
  • Zhang, T.

Abstract

We use the continuity theorem of Lyons for rough paths in the p-variation topology to produce an elementary approach to the large deviation principle and the support theorem for diffusion processes. The proofs reduce to establish the corresponding results for Brownian motion itself as a rough path in the p-variation topology, 2

Suggested Citation

  • Ledoux, M. & Qian, Z. & Zhang, T., 2002. "Large deviations and support theorem for diffusion processes via rough paths," Stochastic Processes and their Applications, Elsevier, vol. 102(2), pages 265-283, December.
    • Handle: RePEc:eee:spapps:v:102:y:2002:i:2:p:265-283
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    Cited by:

    1. Deuschel, Jean-Dominique & Friz, Peter K. & Maurelli, Mario & Slowik, Martin, 2018. "The enhanced Sanov theorem and propagation of chaos," Stochastic Processes and their Applications, Elsevier, vol. 128(7), pages 2228-2269.
    2. Gautier, Eric, 2005. "Uniform large deviations for the nonlinear Schrodinger equation with multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 115(12), pages 1904-1927, December.
    3. Bardina, X. & Nourdin, I. & Rovira, C. & Tindel, S., 2010. "Weak approximation of a fractional SDE," Stochastic Processes and their Applications, Elsevier, vol. 120(1), pages 39-65, January.
    4. Cont, Rama & Kalinin, Alexander, 2020. "On the support of solutions to stochastic differential equations with path-dependent coefficients," Stochastic Processes and their Applications, Elsevier, vol. 130(5), pages 2639-2674.
    5. Yuzuru Inahama, 2010. "A Stochastic Taylor-Like Expansion in the Rough Path Theory," Journal of Theoretical Probability, Springer, vol. 23(3), pages 671-714, September.

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