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August, 1985 On Regularity of Banach-Valued Processes
Nikos E. Frangos
Ann. Probab. 13(3): 985-990 (August, 1985). DOI: 10.1214/aop/1176992919


For the study of the paths of stochastic processes, the upcrossing-down-crossing arguments are available in the real-valued case but not in the vector-valued case. We use in this article stopping time methods and the Kadec-Klee renorming theorem to obtain regularity properties for Banach-lattice valued submartingales and Banach-valued pramarts.


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Nikos E. Frangos. "On Regularity of Banach-Valued Processes." Ann. Probab. 13 (3) 985 - 990, August, 1985.


Published: August, 1985
First available in Project Euclid: 19 April 2007

zbMATH: 0575.60004
MathSciNet: MR799433
Digital Object Identifier: 10.1214/aop/1176992919

Primary: 60B12
Secondary: 60G17 , 60G44 , 60G48

Keywords: order continuous Banach lattice , pramart , regularity of paths , renorming , right and left limits , stopping time , submartingale

Rights: Copyright © 1985 Institute of Mathematical Statistics

Vol.13 • No. 3 • August, 1985
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