Ito's formula for C1,λ-functions of a cadlag process and related calculus

• 成果类型: Article
• 署名作者: Errami, M; Russo, F; Vallois, P
• 署名单位: Universite Paris 13; Universite de Lorraine
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s004400100168
• 发表日期: 2002
• 页码: 191-221
• 关键词: stochastic calculus; SEMIMARTINGALES

摘要

This article develops a framework of stochastic calculus with respect to a cadlag finite quadratic variation process. We apply it to the study of a generalization of a semi-martingale driven SDE studied by Kurtz, Pardoux and Protter [KPP]. We prove an Ito's formula for functions f(X) of a semimartingale with jumps when f has weak smoothness properties. Examples of X for which this formula is valid are time reversible semimartingales and solutions of [KPP] equations driven by Levy processes, provided the sum of the absolute values of the jumps, raised to the power 1 + lambda is a.s. finite, where lambda takes values between 0 and 1.