Occupation time limits of inhomogeneous Poisson systems of independent particles

Abstract

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 Lévy 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 $\gamma <d<\alpha$ leads to an extension of fractional Brownian motion.

22 pages

References in corpus (1)

• Some extensions of fractional Brownian motion and sub-fractional Brownian motion related to particle systems

Cited by in corpus (14)

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