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Backward problems for stochastic differential equations on the Sierpinski gasket

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  • Liu, Xuan
  • Qian, Zhongmin

Abstract

In this paper, we study the non-linear backward problems (with deterministic or stochastic durations) of stochastic differential equations on the Sierpinski gasket. We prove the existence and uniqueness of solutions of backward stochastic differential equations driven by Brownian martingale (defined in Section 2) on the Sierpinski gasket constructed by S. Goldstein and S. Kusuoka. The exponential integrability of quadratic processes for martingale additive functionals is obtained, and as an application, a Feynman–Kac representation formula for weak solutions of semi-linear parabolic PDEs on the gasket is also established.

Suggested Citation

  • Liu, Xuan & Qian, Zhongmin, 2018. "Backward problems for stochastic differential equations on the Sierpinski gasket," Stochastic Processes and their Applications, Elsevier, vol. 128(10), pages 3387-3418.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:10:p:3387-3418
    DOI: 10.1016/j.spa.2017.11.002
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    References listed on IDEAS

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    1. Hinz, Michael & Röckner, Michael & Teplyaev, Alexander, 2013. "Vector analysis for Dirichlet forms and quasilinear PDE and SPDE on metric measure spaces," Stochastic Processes and their Applications, Elsevier, vol. 123(12), pages 4373-4406.
    2. Stoica, I. L., 2003. "A probabilistic interpretation of the divergence and BSDE's," Stochastic Processes and their Applications, Elsevier, vol. 103(1), pages 31-55, January.
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    Cited by:

    1. Yang Yu & Xiaochuan Luo & Huaxi (Yulin) Zhang & Qingxin Zhang, 2019. "The Solution of Backward Heat Conduction Problem with Piecewise Linear Heat Transfer Coefficient," Mathematics, MDPI, vol. 7(5), pages 1-17, April.

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