A NEW FORMULA FOR SOME LINEAR STOCHASTIC EQUATIONS WITH APPLICATIONS

• 成果类型: Article
• 署名作者: Kella, Offer; Yor, Marc
• 署名单位: Hebrew University of Jerusalem; Sorbonne Universite; Universite Paris Cite
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/09-AAP637
• 发表日期: 2010
• 页码: 367-381
• 关键词: continuity properties; INTEGRALS; distributions; stationarity

摘要

We give a representation of the solution for a stochastic linear equation of the form X-t = Y-t + integral((0,t]) X-s-dZ(s) where Z is a cadlag semimartingale and Y is a cadlag adapted process with bounded variation on finite intervals. As an application we study the case where Y and -Z are nondecreasing, jointly have stationary increments and the jumps of -Z are bounded by 1. Special cases of this process are shot-noise processes, growth collapse (additive increase, multiplicative decrease) processes and clearing processes. When Y and Z are, in addition, independent Levy processes, the resulting X is called a generalized Ornstein-Uhlenbeck process.