Cluster continuous time random walks

In a continuous time random walk (CTRW), a random waiting time pre- cedes each random jump. The CTRW model is useful in physics, to model diusing par- ticles. Its scaling limit is a time-changed process, whose densities solve an anomalous diusion equation. This paper develops limit theory and governing equations for cluster CTRW, in which a random number of jumps cluster together into a single jump. The clus- tering introduces a dependence between the waiting times and jumps that significantly aects the asymptotic limit. Vector jumps are considered, along with oracle CTRW, where the process anticipates the next jump.