A LIMIT THEOREM FOR MOMENTS IN SPACE OF THE INCREMENTS OF BROWNIAN LOCAL TIME

• 成果类型: Article
• 署名作者: Campese, Simon
• 署名单位: University of Rome Tor Vergata
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/16-AOP1093
• 发表日期: 2017
• 页码: 1512-1542
• 关键词: l-2 modulus; real line; martingale; continuity; INTEGRALS; LAWS; clt

摘要

We prove a limit theorem for moments in space of the increments of Brownian local time. As special cases for the second and third moments, previous results by Chen et al. [Ann. Prob. 38 (2010) 396-438] and Rosen [Stoch. Dyn. 11 (2011) 5-48], which were later reproven by Hu and Nualart [Electron. Commun. Probab. 15 (2010) 396-410] and Rosen [In Seminaire de Probabilites XLIII (2011) 95-104 Springer] are included. Furthermore, a conjecture of Rosen for the fourth moment is settled: In comparison to the previous methods of proof, we follow a fundamentally different approach by exclusively working in the space variable of the Brownian local time, which allows to give a unified argument for arbitrary orders. The main ingredients are Perkins' semimartingale decomposition, the Kailath-Segall identity and an asymptotic Ray-Knight theorem by Pitman and Yor.