Invariant transports of stationary random measures and mass-stationarity

By Günter Last, Hermann Thorisson. 2009

70 citations recorded by the source corpus.

We introduce and discuss balancing invariant transports of stationary random measures on a Polish Abelian group. The first main result is an associated fundamental invariance property of Palm measures, derived from a generalization of Neveu’s exchange formula. The second main result is a simple sufficient and necessary criterion for the existence of balancing invariant transports. We then introduce (in a non-stationary setting) the concept of mass-stationarity with respect to a random measure, formalizing the intuitive idea that the origin is a typical location in the mass. The third main result of the paper is that a measure is a Palm measure if and only if it is mass-stationary.

Subfields: Finance, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/8b28facb1a23b342ce0fe1595abef73de731d596

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In Finance

Mathew D. Penrose

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Lectures on the Poisson Process (2017, background): “A discussion of balancing more general jointly stationary random measures can be found in [93] and [64].”