STOCHASTIC INTEGRATION WITH RESPECT TO CYLINDRICAL LEVY PROCESSES

• 成果类型: Article
• 署名作者: Jakubowski, Adam; Riedle, Markus
• 署名单位: Nicolaus Copernicus University; University of London; King's College London
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/16-AOP1164
• 发表日期: 2017
• 页码: 4273-4306
• 关键词: limit-theorems; banach-spaces; sums

摘要

A cylindrical Levy process does not enjoy a cylindrical version of the semimartingale decomposition which results in the need to develop a completely novel approach to stochastic integration. In this work, we introduce a stochastic integral for random integrands with respect to cylindrical Levy processes in Hilbert spaces. The space of admissible integrands consists of caglad, adapted stochastic processes with values in the space of Hilbert-Schmidt operators. Neither the integrands nor the integrator is required to satisfy any moment or boundedness condition. The integral process is characterised as an adapted, Hilbert space valued semimartingale with cadlag trajectories.