STRONG EXISTENCE AND UNIQUENESS FOR STABLE STOCHASTIC DIFFERENTIAL EQUATIONS WITH DISTRIBUTIONAL DRIFT

• 成果类型: Article
• 署名作者: Athreya, Siva; Butkovsky, Oleg; Mytnik, Leonid
• 署名单位: Indian Statistical Institute; Indian Statistical Institute Kolkata; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Technion Israel Institute of Technology
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/19-AOP1358
• 发表日期: 2020
• 页码: 178-210
• 关键词: weak; sdes; driven; times

摘要

We consider the stochastic differential equation dX(t) = b(X-t) dt + dL(t), where the drift b is a generalized function and L is a symmetric one dimensional alpha-stable Levy processes, alpha is an element of (1, 2). We define the notion of solution to this equation and establish strong existence and uniqueness whenever b belongs to the Besov-Holder space C-beta for beta > 1/2 - alpha 1/2.