Uniqueness in Law for Stable-Like Processes of Variable Order

Peng Jin ()
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Peng Jin: Shantou University

Journal of Theoretical Probability, 2021, vol. 34, issue 2, 522-552

Abstract: 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

Keywords: Stable-like process; Martingale problem; Transition density function; Resolvent; Integro-differential operator; 60J75; 60G52 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10959-020-00988-0

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