| Abstract: |
| We introduce the notion of the concentration function for multi-dimensional L\`evy measures and related notions of level sets, concentration sets, and concentration norms. We will present a systematic study of the concentration and heat kernel properties of multivariate L\`evy processes based on these geometry notions. This study is originated in our previous research of SDEs driven by spatially heterogeneous L\`evy noises. We will present a general approach for getting weak existence/uniqueness and heat kernel estimates for solutions of L\`evy driven SDEs with the assumptions on the coefficients given in the terms of the intrinsic geometry of the driving noise, which unifies and extends considerably the previously available results. |
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