A parametrix approach for some degenerate stable driven SDEs

作者:Huang Lorick*; Menozzi Stephane
来源:Annales de l Institut Henri Poincare-Probabilites et Statistiques, 2016, 52(4): 1925-1975.
DOI:10.1214/15-AIHP704

摘要

We consider a stable driven degenerate stochastic differential equation, whose coefficients satisfy a kind of weak Hormander condition. Under mild smoothness assumptions we prove the uniqueness of the martingale problem for the associated generator under some dimension constraints. Also, when the driving noise is scalar and tempered, we establish density bounds reflecting the multi-scale behavior of the process.

  • 出版日期2016-11