ORACLE CONTINUOUS TIME RANDOM WALKS

In a continuous time random walk (CTRW), a random waiting time precedes each random jump. The CTRW model is useful in physics, to model dif- fusing particles. Its scaling limit is a time-changed process, whose densities solve an anomalous diusion equation. Some applications require the anticipating version, an oracle continuous time random walk (OCTRW), where the next jump after any given time is also included. This paper develops limit theory and governing equa- tions for the OCTRW, which can be quite dierent from the non-anticipating case if the waiting time and the subsequent jump are dependent random variables.