Advances and Applications in Statistics
Volume 44, Issue 1, Pages 57 - 76
(January 2015) http://dx.doi.org/10.17654/ADASJan2015_057_076 |
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SOME CLASSICAL-NEW RESULTS ON THE SET-INDEXED BROWNIAN MOTION
Arthur Yosef
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Abstract: In this article, we extend many results from classical Brownian motion to set-indexed Brownian motion; most of the proofs are performed by “characterization of set-indexed Brownian motion by flows”, which says that a square-integrable set-indexed stochastic process is a set- indexed Brownian motion if and only if its projection on all the strictly increasing continuous paths are one-parameter time-change Brownian motions. |
Keywords and phrases: set-indexed process, Brownian motion, increasing path. |
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