ITO'S FORMULA FOR GAUSSIAN PROCESSES WITH STOCHASTIC DISCONTINUITIES

• 成果类型: Article
• 署名作者: Bender, Christian
• 署名单位: Saarland University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/19-AOP1369
• 发表日期: 2020
• 页码: 458-492
• 关键词: fractional brownian-motion; calculus; Respect; integration

摘要

We introduce a Skorokhod type integral and prove an Ito formula for a wide class of Gaussian processes which may exhibit stochastic discontinuities. Our Ito formula unifies and extends the classical one for general (i.e., possibly discontinuous) Gaussian martingales in the sense of Ito integration and the one for stochastically continuous Gaussian non-martingales in the Skorokhod sense, which was first derived in Ales et al.