Mathematics – Probability
Scientific paper
2006-10-14
Mathematics
Probability
Scientific paper
We consider the linear integro-differential operator $L$ defined by \[ Lu(x) =\int_\Rn (u(x+y) - u(x) - 1_{[1,2]}(\alpha) 1_{\{|y|\leq 2\}}(y)y \cdot \nabla u(x)) k(x,y) \sd y . \] Here the kernel $k(x,y)$ behaves like $|y|^{-d-\alpha}$, $\alpha \in (0,2)$, for small $y$ and is H\"older-continuous in the first variable, precise definitions are given below. The aim of this work is twofold. On one hand, we study the unique solvability of the Cauchy problem corresponding to $L$. On the other hand, we study the martingale problem for $L$. The analytic results obtained for the deterministic parabolic equation guarantee that the martingale problem is well-posed. Our strategy follows the classical path of Stroock-Varadhan. The assumptions allow for cases that have not been dealt with so far.
No associations
LandOfFree
The Cauchy problem and the martingale problem for integro-differential operators with non-smooth kernels does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Cauchy problem and the martingale problem for integro-differential operators with non-smooth kernels, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Cauchy problem and the martingale problem for integro-differential operators with non-smooth kernels will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-89990