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

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

2007-12-26

arxiv.org/abs/0712.4137v2

Mathematics

Probability

Scientific paper

Let $L$ be the operator defined on $C^2$ functions by $$L f(x)=\int[f(x+h)-f(x)-1_{(|h|\leq 1)}\nabla f(x)\cdot h]\frac{n(x,h)}{|h|^{d+\alpha(x)}}dh.$$ 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.

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