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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENTAL SEMINAR}
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\centerline{4:15 p.m., Thursday, August 17, 2000}
\centerline{Sequoia Hall Rm. 200}

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\centerline{\sl Hermann Thorisson}
\centerline{\sl Science Institute}
\centerline{\sl University of Iceland}
\centerline{\sl 107 Reykjavik}
\centerline{\sl Iceland}
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\centerline{\bf Point-Stationarity in $d$ Dimensions and Palm Theory}
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Point-stationarity formalizes the intuitive idea of a simple point process
in $R^d$ for which the behaviour relative to a given {\it point of the
process} is independent of the point selected as origin. (Note that this is
different from stationarity, which means that the behaviour of the process
relative to a given {\it non-random} site in $R^d$ is independent of the
site selected as origin). 

For $d = 1$, point-stationarity has a straightforward definition: it means
distributional invariance under shifts of the origin to the $n$th point on
the right (or left) of the point at 0 (for instance, a stationary Poisson
process becomes point-stationary if we add a point at 0). For  $d > 1$,
this definition clearly does not work. But is there some similar way to
move between 
points in higher dimension? Think about it. 

In this talk we give meaning to (that is, define) point-stationarity in $d
> 1$ dimensions. Our definition (luckily) turns out to be the
characterizing property of the so-called Palm version of a stationary point
process (as is the case in one dimension). We also show how shift-coupling
has a natural place in this Palm theory.

Reference:

Thorisson, H. (2000). Coupling, Stationarity, and Regeneration. Springer,
NY, [http://www.hi.is/~hermann]

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