Uniqueness for the martingale problem associated with pure jump processes of variable order

arXiv0712.4137MaRDI QIDQ6207937

Huili Tang

Publication date: 26 December 2007

Abstract: Let $L$ be the operator defined on $C^2$ functions by ${\displaystyle }$L f(x)=int[f(x+h)-f(x)-1_{(|h|leq 1)} abla f(x)cdot h]frac{n(x,h)}{|h|^{d+alpha(x)}}dh.${\displaystyle }$ This is an operator of variable order and the corresponding process is of pure jump type. We consider the martingale problem associated with $L$. Sufficient conditions for existence and uniqueness are given. Transition density estimates for $alpha$-stable processes are also obtained.

Mathematics Subject Classification ID

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