一类退化稳定驱动SDEs的参数化方法

IF 1.2 2区数学 Q2 STATISTICS & PROBABILITY

Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2014-02-17 DOI:10.1214/15-AIHP704

Lorick Huang, S. Menozzi

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引用次数: 25

摘要

考虑一类系数满足弱Hormander条件的稳定驱动退化随机微分方程。在温和平滑的假设下，我们证明了相关生成器的鞅问题在一些维数约束下的唯一性。此外，当驱动噪声为标量调质时，我们建立了反映过程多尺度行为的密度边界。

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A parametrix approach for some degenerate stable driven SDEs

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.

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来源期刊

Annales De L Institut Henri Poincare-probabilites Et Statistiques 数学-统计学与概率论

CiteScore

2.70

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Probability and Statistics section of the Annales de l’Institut Henri Poincaré is an international journal which publishes high quality research papers. The journal deals with all aspects of modern probability theory and mathematical statistics, as well as with their applications.