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On a decomposition of symmetric diffusions with reflecting boundary conditions

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  • Rozkosz, Andrzej

Abstract

We consider a symmetric diffusion corresponding to uniformly elliptic divergence form operator with reflection at the boundary of a domain satisfying the general conditions introduced by Lions and Sznitman. We prove that for each starting point inside the domain the diffusion is a Dirichlet process in the sense of Föllmer and we obtain the Lyons-Zheng-Skorokhod representation of its zero quadratic variation part.

Suggested Citation

  • Rozkosz, Andrzej, 2003. "On a decomposition of symmetric diffusions with reflecting boundary conditions," Stochastic Processes and their Applications, Elsevier, vol. 103(1), pages 101-122, January.
    • Handle: RePEc:eee:spapps:v:103:y:2003:i:1:p:101-122
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    Cited by:

    1. Falkowski, Adrian & Słomiński, Leszek, 2022. "SDEs with two reflecting barriers driven by semimartingales and processes with bounded p-variation," Stochastic Processes and their Applications, Elsevier, vol. 146(C), pages 164-186.
    2. Falkowski, Adrian & Słomiński, Leszek, 2017. "SDEs with constraints driven by semimartingales and processes with bounded p-variation," Stochastic Processes and their Applications, Elsevier, vol. 127(11), pages 3536-3557.
    3. Słomiński, Leszek, 2013. "Weak and strong approximations of reflected diffusions via penalization methods," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 752-763.

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