We thank Professor Grigoriu and Dr. Uy for their insightful discussion [1] of our review article. They complement our review by discussing two important topics: (i) extreme events in dynamical systems driven by random stochastic excitations and (ii) multivariate extreme value theory to assess the quality of indicators of extreme events. Here, we close by adding a few additional comments on each topic.
The main focus in our review was on deterministic nonlinear systems where extreme events occur spontaneously as a result of nontrivial interactions between various degrees-of-freedom [2–4]. Grigoriu and Uy [1] correctly point out that extreme events can also take place in dynamical systems driven by heavy-tailed stochastic excitations. They demonstrate this with a simple example, the linear stochastic differential equation
