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Uniqueness in Law for Stable-Like Processes of Variable Order

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  • Peng Jin

    (Shantou University)

Abstract

Let $$d\ge 1$$ d ≥ 1 . Consider a stable-like operator of variable order $$\begin{aligned} {\mathcal {A}}f(x)&=\int _{{\mathbb {R}}^{d}\backslash \{0\}} \left[ f(x+h)-f(x)-\mathbf {1}_{\{|h|\le 1\}}h\cdot \nabla f(x)\right] n(x,h)|h|^{-d-\alpha (x)}\mathrm{d}h, \end{aligned}$$ A f ( x ) = ∫ R d \ { 0 } f ( x + h ) - f ( x ) - 1 { | h | ≤ 1 } h · ∇ f ( x ) n ( x , h ) | h | - d - α ( x ) d h , where $$0

Suggested Citation

  • Peng Jin, 2021. "Uniqueness in Law for Stable-Like Processes of Variable Order," Journal of Theoretical Probability, Springer, vol. 34(2), pages 522-552, June.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:2:d:10.1007_s10959-020-00988-0
    DOI: 10.1007/s10959-020-00988-0
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    References listed on IDEAS

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    1. Chen, Zhen-Qing & Kumagai, Takashi, 2003. "Heat kernel estimates for stable-like processes on d-sets," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 27-62, November.
    2. Jamil Chaker, 2019. "The martingale problem for a class of nonlocal operators of diagonal type," Mathematische Nachrichten, Wiley Blackwell, vol. 292(11), pages 2316-2337, November.
    3. T. Uemura, 2004. "On Symmetric Stable-Like Processes: Some Path Properties and Generators," Journal of Theoretical Probability, Springer, vol. 17(3), pages 541-555, July.
    4. Bass, Richard F. & Tang, Huili, 2009. "The martingale problem for a class of stable-like processes," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1144-1167, April.
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