Speaker
Description
Continuous-time random walks (CTRWs) with stochastic resetting provide a natural framework for modelling anomalous transport under intermittent restart mechanisms. In this seminar, we present recent asymptotic results for CTRWs with resetting under suitable space–time scaling limits. For heavy-tailed waiting times and jumps in the domain of attraction of stable laws, we show convergence to an $\alpha$-stable process time-changed by the inverse of a $\beta$-stable subordinator, combined with a resetting structure inherited from the original dynamics. We also discuss functional convergence in the Skorokhod $J_1$ topology, based on a pathwise construction via concatenation of independent excursions. Finally, we examine the effect of scaling the resetting mechanism itself, showing that different asymptotic regimes lead either to an equilibrium random limit or to a nontrivial time-rescaled CTRW with resetting.
