By analyzing physically meaningful solutions of a generalized one-dimensional Fokker-Planck equation, I show that a broad class of random motions can be described within a unified framework. The approach recovers a variety of stochastic processes, ranging from Brownian diffusion to active motion, and including anomalous transport, stochastic resetting, and trapping mechanisms.
Noise-driven dynamics in single-well potentials can produce bimodal, or more generally multimodal, stationary states. The emergence of multimodality depends sensitively on the properties of the driving noise. Such behavior is typically associated with systems subject to strong fluctuations, for example those driven by Lévy noise, or with systems driven by temporally correlated noise, such as...
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...
