A limit theorem for moments in space of the increments of Brownian local time

• Simon Campese ^[1]
  1. [1] Università di Roma Tor Vergata
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 45, Nº. 3, 2017, págs. 1512-1542
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • 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 Séminaire de Probabilités 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.