Extremes in dynamic-stochastic systems.

Extreme events capture the attention and imagination of the general public. Extreme events, especially meteorological and climatological extremes, cause significant economic damages and lead to a significant number of casualties each year. Thus, the prediction of extremes is of obvious importance. Here, I will survey the predictive skill and the predictability of extremes using dynamic-stochastic models. These dynamic-stochastic models combine deterministic nonlinear dynamics with a stochastic component, which consists potentially of both additive and multiplicative noise components. In these models, extremes are created by either the nonlinear dynamics, multiplicative noise, or additive heavy-tailed noises. These models naturally capture the observed clustering of extremes and can be used for the prediction of extremes.