The chaotic-representation property for a class of normal martingales

• 成果类型: Article
• 署名作者: Attal, Stephane; Belton, Alexander C. R.
• 署名单位: University College Cork; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-006-0052-z
• 发表日期: 2007
• 页码: 543-562
• 关键词: azema martingales; filtrations; FORMULA

摘要

Suppose Z = (Zt) (t >= 0) is a normal martingale which satisfies the structure equation d[Z](t) = (alpha(t) + beta(t)Z(t-))dZ(t) + dt. By adapting and extending techniques due to Parthasarathy and to Kurtz, it is shown that, if alpha is locally bounded and beta has values in the interval [- 2,0], the process Z is unique in law, possesses the chaotic- representation property and is strongly Markovian ( in an appropriate sense). If also beta is bounded away from the endpoints 0 and 2 on every compact subinterval of [ 0,infinity[ then Z is shown to have locally bounded trajectories, a variation on a result of Russo and Vallois.