Extremes of q-Ornstein–Uhlenbeck processes

Extremes of supOU processes

Barndorff-Nielsen and Shephard [3] investigate supOU processes as volatility models. Empirical volatility has tails heavier than normal, long memory in the sense that the empirical autocorrelation function decreases slower than exponential, and exhibits volatility clusters on high levels. We investigate supOU processes with respect to these stylized facts. The class of supOU processes is vast a...

Extremes of Independent Gaussian Processes

For every n ∈ N, let X1n, . . . , Xnn be independent copies of a zero-mean Gaussian process Xn = {Xn(t), t ∈ T}. We describe all processes which can be obtained as limits, as n → ∞, of the process an(Mn − bn), where Mn(t) = maxi=1,...,n Xin(t) and an, bn are normalizing constants. We also provide an analogous characterization for the limits of the process anLn, where Ln(t) = mini=1,...,n |Xin(t)|.

Extremes of Mixed Environmental Processes

SUMMARY Models for the behaviour of environmental processes at extreme levels are vital for the design of defences against the rarest events which are liable to occur. A range of classical techniques have been developed to estimate high quantiles in the distributions of stationary and non{stationary series, but these generally suuer from a scarcity of data at the most extreme levels. Recently d...

Extremes of Continuous-Time Processes

In this paper we present a review on the extremal behavior of stationary continuous-time processes with emphasis on generalized Ornstein-Uhlenbeck processes. We restrict our attention to heavy-tailed models like heavy-tailed Ornstein-Uhlenbeck processes or continuous-time GARCH processes. The survey includes the tail behavior of the stationary distribution, the tail behavior of the sample maxim...

Extremes of Moving Averages of Stable Processes