A group action on increasing sequences of set-indexed Brownian motions

Arthur Yosef

doi:10.15559/15-vmsta31

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arXiv · 1508.02858

A group action on increasing sequences of set-indexed Brownian motions

Arthur Yosef

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Abstract

We prove 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 sequences are one-parameter $G$-time-changed Brownian motions. In addition, we study the "sequence-independent variation" property for group stationary-increment stochastic processes in general and for a set-indexed Brownian motion in particular. We present some applications.

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Arthur Yosef. 2015-08-12. A group action on increasing sequences of set-indexed Brownian motions. https://doi.org/10.15559/15-vmsta31

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