具有Hölder漂移的简并SDE的强存在唯一性

IF 1.2 2区数学 Q2 STATISTICS & PROBABILITY

Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2017-02-01 DOI:10.1214/15-AIHP716

P. C. D. Raynal

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引用次数: 30

摘要

．在本文中，我们证明了具有Hölder漂移的随机退化系统，当Hölder指数大于临界值2 / 3时的路径唯一性。这项工作将Zvonkin (Mat. Sb. (N.S.) 93(135)(1974) 129 - 149,152)、Veretennikov (Mat. Sb. (N.S.) 111(153)(1980) 434 - 452,480)、Krylov和Röckner (Probab。理论相关领域131(2)(2005)154-196)从非简并到简并情况。在退化情况下，Hölder指数阈值的存在可以理解为平衡噪声的退化所付出的代价。我们的证明依赖于相关PDE的正则化性质，该PDE在当前框架中是退化的，并且基于参数矩阵方法。的简历。(L 'apparition用品seuil批判倒L 'exposant可能vue像价格付款人倒上拉degenerescence。根据不同的参数，根据不同的参数，根据不同的参数，根据不同的参数，根据不同的参数，根据不同的参数，根据不同的参数，确定不同的参数。

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Strong existence and uniqueness for degenerate SDE with Hölder drift

. In this paper, we prove pathwise uniqueness for stochastic degenerate systems with a Hölder drift, for a Hölder exponent larger than the critical value 2 / 3. This work extends to the degenerate setting the earlier results obtained by Zvonkin ( Mat. Sb. (N.S.) 93(135) (1974) 129–149, 152), Veretennikov ( Mat. Sb. (N.S.) 111(153) (1980) 434–452, 480), Krylov and Röckner ( Probab. Theory Related Fields 131 (2) (2005) 154–196) from non-degenerate to degenerate cases. The existence of a threshold for the Hölder exponent in the degenerate case may be understood as the price to pay to balance the degeneracy of the noise. Our proof relies on regularization properties of the associated PDE, which is degenerate in the current framework and is based on a parametrix method. Résumé. ( L’apparition d’un seuil critique pour l’exposant peut-être vue comme le prix à payer pour la dégénérescence. La preuve repose sur des résultats de régularité de la solution de l’EDP associée, qui est dégénérée, et est basée sur une méthode parametrix.

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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.