Functional central limit theorem for the occupation time of the origin for branching random walks $dge 3$
- Birkner, Matthias
- Zähle, Iljana
2010 Mathematics Subject Classification
- Branching random walk, occupation time, functional central limit theorem
We show that the centred occupation time process of the origin of a system of critical binary branching random walks in dimension $d ge 3$, started off either from a Poisson field or in equilibrium, when suitably normalised, converges to a Brownian motion in $d ge 4$. In $d=3$, the limit process is fractional Brownian motion with Hurst parameter $3/4$ when starting in equilibrium, and a related Gaussian process when starting from a Poisson field.
- Ann. Probab., 35 (2007) pp. 2063-2090.