The martingale problem for a class of stable-like processes

Details The martingale problem for a class of stable-like processes The martingale problem for a class of stable-like processes

2007-09-19

arxiv.org/abs/0709.3082v1

Mathematics

Probability

Scientific paper

Let $\alpha\in (0,2)$ and consider the operator $$L f(x) =\int
[f(x+h)-f(x)-1_{(|h|\leq 1)} \nabla f(x)\cdot h] \frac{A(x,h)}{|h|^{d+\alpha}}
dh, $$ where the $\nabla f(x)\cdot h$ term is omitted if $\alpha<1$. We
consider the martingale problem corresponding to the operator $L$ and under
mild conditions on the function $A$ prove that there exists a unique solution.

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