Aspects of Extreme Value Theory for Stationary Processes - a Survey
نویسنده
چکیده
SUMMARY The primary concern in this paper is with the distributional results of classical extreme value theory, anc their developMent to apply to stationary processes. The main emphasis is on stationary sequences, where the theory is \'lell developed. :\esults available for continuous parameter processes are also described, but with particular reference to stationary normal processes.
منابع مشابه
Stationary Markov Processes
We consider some classes of stationary, counting{measure{valued Markov processes and their companions under time{reversal. Examples arise in the L evy{It^ o decomposition of stable Ornstein{Uhlenbeck processes, the large{time asymptotics of the standard additive coalescent, and extreme value theory. These processes share the common feature that points in the support of the evolving counting{ me...
متن کاملOn Sampling of Stationary Increment Processes
Under a complex technical condition, similar to such used in extreme value theory, we find the rate q(ε) at which a stochastic process with stationary increments ξ should be sampled, for the sampled process ξ(⌊·/q(ε)⌋q(ε)) to deviate from ξ by at most ε, with a given probability, asymptotically as ε ↓ 0. The canonical application is to discretization errors in computer simulation of stochastic ...
متن کاملOn Approximate Stationary Radial Solutions for a Class of Boundary Value Problems Arising in Epitaxial Growth Theory
In this paper, we consider a non-self-adjoint, singular, nonlinear fourth order boundary value problem which arises in the theory of epitaxial growth. It is possible to reduce the fourth order equation to a singular boundary value problem of second order given by w''-1/r w'=w^2/(2r^2 )+1/2 λ r^2. The problem depends on the parameter λ and admits multiple solutions. Therefore, it is difficult to...
متن کاملSecond Moment of Queue Size with Stationary Arrival Processes and Arbitrary Queue Discipline
In this paper we consider a queuing system in which the service times of customers are independent and identically distributed random variables, the arrival process is stationary and has the property of orderliness, and the queue discipline is arbitrary. For this queuing system we obtain the steady state second moment of the queue size in terms of the stationary waiting time distribution of a s...
متن کاملThe Stationary - NonStationary Process and The Variable Roots Difference Equations
Stochastic, processes can be stationary or nonstationary. They depend on the magnitude of shocks. In other words, in an auto regressive model of order one, the estimated coefficient is not constant. Another finding of this paper is the relation between estimated coefficients and residuals. We also develop a catastrophe and chaos theory for change of roots from stationary to a nonstationary one ...
متن کامل