A group action on increasing sequences of set-indexed Brownian motions
Volume 2, Issue 2 (2015), pp. 185–198
Pub. online: 6 August 2015
Type: Research Article
Open Access
Open Access
Received
23 February 2015
23 February 2015
Revised
29 July 2015
29 July 2015
Accepted
30 July 2015
30 July 2015
Published
6 August 2015
6 August 2015
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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