Frechet-valued martingales and stochastic integrals
作者:
T. E. Duncan,
期刊:
Stochastics
(Taylor Available online 1975)
卷期:
Volume 1,
issue 1-4
页码: 269-284
ISSN:0090-9491
年代: 1975
DOI:10.1080/17442507508833110
出版商: Gordon and Breach Science Publishers, Ltd
关键词: Martingales;stochastic integrals;Brownian motion
数据来源: Taylor
摘要:
Stochastic processes with values in a separable Frechet space whose a itinuous linear functional are real-valued square integrable martingales are investigated. The coordinate measures on the Fréchet space are obtained from cylinder set measures on a Hilbert space that is dense in the Fréchet space. Real-valued stochastic integrals are defined from the Fréchet-valued martingales using integrands from the topological dual of the aforementioned Hilbert space. An increasing process with values in the self adjoint operators on the Hilbert space plays a fundamental role in the definition of stochastic integrals. For Banach-valued Brownian motion the change of variables formula of K. Itô is generalized. A converse to the construction of the measures on the Fréchet space from cylinder set measures on a Hilbert space is also obtained.
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