The martingale problem for geometric stable-like processes
| Autor: | Iyer, Sarvesh Ravichandran |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | We prove that the martingale problem is well posed for pure-jump L\'evy-type operators of the form $$ (\mathcal Lf)(x) = \int_{\mathbb R^d \setminus \{0\}} \left(f(x+h)-f(x) - (\nabla f(x) \cdot h)1_{\|h\| < 1}\right)K(x,h) dh, $$ where $K(x,\cdot)$ is a jump kernel of the form $K(x,h) \sim \frac{l(\|h\|)}{\|h\|^d}$ for each $x \in \mathbb R^d,\|h\|<1$, and $l$ is a positive function that is slowly varying at $0$, under suitable assumptions on $K$. This includes jump kernels such as those of $\alpha$-geometric stable processes, $\alpha \in (0,2]$. Comment: 29 pages, to be submitted to Stochastic Processes and Applications |
| Databáze: | arXiv |
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