Occupation time limits of inhomogeneous Poisson systems of independent particles

Details Occupation time limits of inhomogeneous Poisson systems of independent particles Occupation time limits of inhomogeneous Poisson systems of independent particles

2006-09-11

arxiv.org/abs/math/0609290v1

Stochastic Process. Appl. 118 (2008), no. 1, 28-52

Mathematics

Probability

22 pages

Scientific paper

10.1016/j.spa.2007.03.008

We prove functional limits theorems for the occupation time process of a system of particles moving independently in $R^d$ according to a symmetric $\alpha$-stable L\'evy process, and starting off from an inhomogeneous Poisson point measure with intensity measure $\mu(dx)=(1+|x|^{\gamma})^{-1}dx,\gamma>0$, and other related measures. In contrast to the homogeneous case $(\gamma=0)$, the system is not in equilibrium and ultimately it vanishes, and there are more different types of occupation time limit processes depending on arrangements of the parameters $\gamma, d$ and $\alpha$. The case $\gamma

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