Extremes of Gaussian processes over an infinite horizon
نویسندگان
چکیده
منابع مشابه
Extremes of Gaussian processes over an infinite horizon
Consider a centered separable Gaussian process Y with a variance function that is regularly varying at infinity with index 2H ∈ (0, 2). Let φ be a ‘drift’ function that is strictly increasing, regularly varying at infinity with index β > H, and vanishing at the origin. Motivated by queueing and risk models, we investigate the asymptotics for u→∞ of the probability P (sup t≥0 Yt − φ(t) > u) as u...
متن کاملExtremes 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)|.
متن کاملCharacterization and computation of infinite-horizon specifications over Markov processes
This work is devoted to the formal verification of specifications over general discrete-time Markov processes, with an emphasis on infinite-horizon properties. These properties, formulated in a modal logic known as PCTL, can be expressed through value functions defined over the state space of the process. The main goal is to understand how structural features of the model (primarily the presenc...
متن کاملMoney and indeterminacy over an infinite horizon
Money provides liquidity services through a cash-in-advance constraint. The exchange of commodities and assets extends over an infinite horizon under uncertainty and a complete asset market. Monetary policy sets the path of rates of interest and accommodates the demand for balances. Competitive equilibria exist. But, for a fixed path of rates of interest, there is a non-trivial multiplicity of ...
متن کاملOptimal Control for Partially Observable Markov Decision Processes over an Infinite Horizon
In this paper we consider an optimal control problem for partially observable Markov decision processes with finite states, signals and actions OVE,r an infinite horizon. It is shown that there are €optimal piecewise·linear value functions and piecl~wise-constant policies which are simple. Simple means that there are only finitely many pieces, each of which is defined on a convex polyhedral set...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 2005
ISSN: 0304-4149
DOI: 10.1016/j.spa.2004.09.005