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Boundary Harnack principle for subordinate Brownian motions

Author

Listed:
  • Kim, Panki
  • Song, Renming
  • Vondracek, Zoran

Abstract

We establish a boundary Harnack principle for a large class of subordinate Brownian motions, including mixtures of symmetric stable processes, in [kappa]-fat open sets (disconnected analogue of John domains). As an application of the boundary Harnack principle, we identify the Martin boundary and the minimal Martin boundary of bounded [kappa]-fat open sets with respect to these processes with their Euclidean boundaries.

Suggested Citation

  • Kim, Panki & Song, Renming & Vondracek, Zoran, 2009. "Boundary Harnack principle for subordinate Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1601-1631, May.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:5:p:1601-1631
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    Citations

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    Cited by:

    1. Chen, Zhen-Qing & Wang, Jie-Ming, 2022. "Boundary Harnack principle for diffusion with jumps," Stochastic Processes and their Applications, Elsevier, vol. 151(C), pages 342-395.
    2. Kim, Panki & Song, Renming & Vondraček, Zoran, 2013. "Potential theory of subordinate Brownian motions with Gaussian components," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 764-795.
    3. Farouk Mselmi, 2022. "Generalized linear model for subordinated Lévy processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 772-801, June.
    4. Kwaśnicki, Mateusz & Małecki, Jacek & Ryznar, Michał, 2013. "First passage times for subordinate Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1820-1850.
    5. Grzywny, Tomasz & Kwaśnicki, Mateusz, 2018. "Potential kernels, probabilities of hitting a ball, harmonic functions and the boundary Harnack inequality for unimodal Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 128(1), pages 1-38.
    6. Kim, Panki & Lee, Yunju, 2013. "Oscillation of harmonic functions for subordinate Brownian motion and its applications," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 422-445.
    7. Fotopoulos, Stergios & Jandhyala, Venkata & Wang, Jun, 2015. "On the joint distribution of the supremum functional and its last occurrence for subordinated linear Brownian motion," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 149-156.
    8. Kim, Kyung-Youn & Kim, Panki, 2014. "Two-sided estimates for the transition densities of symmetric Markov processes dominated by stable-like processes in C1,η open sets," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 3055-3083.
    9. Chen, Zhen-Qing & Kim, Panki & Song, Renming, 2011. "Green function estimates for relativistic stable processes in half-space-like open sets," Stochastic Processes and their Applications, Elsevier, vol. 121(5), pages 1148-1172, May.

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