• Corpus ID: 238856684

Phase transition for extremes of a family of stationary multiple-stable processes

  title={Phase transition for extremes of a family of stationary multiple-stable processes},
  author={Shuyang Bai and Yizao Wang},
We investigate a family of stationary processes that may exhibit either long-range or short-range dependence, depending on the parameters. The processes can be represented as multiple stable integrals, and there are two parameters for the processes, the memory parameter β ∈ (0, 1) and the multiplicity parameter p ∈ N. We investigate the macroscopic limit of extremes of the process, in terms of convergence of random sup-measures, for the full range of parameters. Our results show that (i) the… 


Structure of stationary stable processes
A connection between structural studies of stationary non-Gaussian stable processes and the ergodic theory of nonsingular flows is established and exploited. Using this connection, a unique
Stable non-Gaussian random processes. Stochastic Modeling
  • 1994
A New Shape of Extremal Clusters For Certain Stationary Semi-Exponential Processes With Moderate Long Range Dependence
Extremal clusters of stationary processes with long memory can be quite intricate. For certain stationary infinitely divisible processes with subexponential tails, including both power-like tails and
Extremal clustering under moderate long range dependence and moderately heavy tails
Stochastic Processes and Long Range Dependence
Classes of mixing stable processes
Stationary self-similar extremal processes
SummaryLet (ξk)k∞=−∞ be a stationary sequence of random variables, and, forA⊂ℝ, let $$M_n (A): = \mathop V\limits_{k/n \in A} \gamma _n (\xi _k )$$ where γn is an affine transformation of ℝ (has the
Extreme Values, Regular Variation, and Point Processes
Contents: Preface * Preliminaries * Domains of Attraction and Norming Constants * Quality of Convergence * Point Processes * Records and Extremal Processes * Multivariate Extremes * References *
Tail processes for stable-regenerative model
We investigate a family of discrete-time stationary processes, known as stable-regenerative model, that may exhibit typical behaviors of short-range or long-range dependence, respectively, depending
Extremal theory for long range dependent infinitely divisible processes
We prove limit theorems of an entirely new type for certain long memory regularly varying stationary infinitely divisible random processes. These theorems involve multiple phase transitions governed