✦ LIBER ✦
A parametrix construction for the fundamental solution of the evolution equation associated with a pseudo-differential operator generating a Markov process
✍ Scribed by Björn Böttcher
- Publisher
- John Wiley and Sons
- Year
- 2005
- Tongue
- English
- Weight
- 138 KB
- Volume
- 278
- Category
- Article
- ISSN
- 0025-584X
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✦ Synopsis
Abstract
We use the method proposed by H. Kumano‐go in the classical case to construct a parametrix of the equation $ \textstyle {{\partial u} \over {\partial t}}$ + q (x, D )u = 0 where q (x, D ) is a pseudo‐differential operator with symbol in the class introduced by W. Hoh. In case where –q (x, D ) extends to a generator of a Feller semigroup our construction yields an approximation for the transition densities of the corresponding Markov process. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)