45 citations · 118 across the 23 of their papers we have counts for
23 papers
Joint sum-max limit for a class of long-range dependent processes with heavy tails
Shuyang Bai, He Tang
We consider a class of stationary processes exhibiting both long-range dependence and heavy tails. Separate limit theorems for sums and for extremes have been established recently…
Optimal Sampling Designs for Multi-dimensional Streaming Time Series with Application to Power Grid Sensor Data
Rui Xie, Shuyang Bai, Ping Ma
The Internet of Things (IoT) system generates massive high-speed temporally correlated streaming data and is often connected with online inference tasks under computational or ener…
Tail Adversarial Stability for Regularly Varying Linear Processes and their Extensions
Shuyang Bai, Ting Zhang
The notion of tail adversarial stability has been proven useful in obtaining limit theorems for tail dependent time series. Its implication and advantage over the classical strong…
Tail processes for stable-regenerative multiple-stable model
Shuyang Bai, Yizao Wang
We investigate a family of discrete-time stationary processes defined by multiple stable integrals and renewal processes with infinite means. The model may exhibit behaviors of sho…
Phase transition for extremes of a family of stationary multiple-stable processes
Shuyang Bai, Yizao Wang
We investigate a family of multiple-stable processes that may exhibit either long-range or short-range dependence, depending on the parameters. There are two parameters for the pro…
Limit Theorems for Conservative Flows on Multiple Stochastic Integrals
Shuyang Bai
We consider a stationary sequence constructed by a multiple stochastic integral and an infinite-measure conservative dynamical system. The random measure defining the multi…
Representations of Hermite processes using local time of intersecting stationary stable regenerative sets
Shuyang Bai
Hermite processes are a class of self-similar processes with stationary increments. They often arise in limit theorems under long-range dependence. We derive new representations of…
A functional non-central limit theorem for multiple-stable processes with long-range dependence
Shuyang Bai, Takashi Owada, Yizao Wang
A functional limit theorem is established for the partial-sum process of a class of stationary sequences which exhibit both heavy tails and long-range dependence. The stationary se…
Sensivity of the Hermite rank
Shuyang Bai, Murad s. Taqqu
The Hermite rank appears in limit theorems involving long memory. We show that an Hermite rank higher than one is unstable when the data is slightly perturbed by transformations su…
Behavior of the generalized Rosenblatt process at extreme critical exponent values
Shuyang Bai, Murad S. Taqqu
The generalized Rosenblatt process is obtained by replacing the single critical exponent characterizing the Rosenblatt process by two different exponents living in the interior of…
How the instability of ranks under long memory affects large-sample inference
Shuyang Bai, Murad S. Taqqu
Under long memory, the limit theorems for normalized sums of random variables typically involve a positive integer called "Hermite rank". There is a different limit for each Hermit…
Hermite rank, power rank and the generalized Weierstrass transform
Shuyang Bai, Murad S. Taqqu
Using the theory of generalized Weierstrass transform, we show that the Hermite rank is identical to the power rank in the Gaussian case, and that an Hermite rank higher than one i…
A unified approach to self-normalized block sampling
Shuyang Bai, Murad S. Taqqu, Ting Zhang
The inference procedure for the mean of a stationary time series is usually quite different under various model assumptions because the partial sum process behaves differently depe…
On the validity of resampling methods under long memory
Shuyang Bai, Murad S. Taqqu
For long-memory time series, inference based on resampling is of crucial importance, since the asymptotic distribution can often be non-Gaussian and is difficult to determine stati…
Short-range dependent processes subordinated to the Gaussian may not be strong mixing
Shuyang Bai, Murad S. Taqqu
There are all kinds of weak dependence. For example, strong mixing. Short-range dependence (SRD) is also a form of weak dependence. It occurs in the context of processes that are s…
The universality of homogeneous polynomial forms and critical limits
Shuyang Bai, Murad S. Taqqu
Nourdin et al. [9] established the following universality result: if a sequence of off-diagonal homogeneous polynomial forms in i.i.d. standard normal random variables converges in…
Constraining quantum critical dynamics: 2+1D Ising model and beyond
William Witczak-Krempa
Quantum critical (QC) phase transitions generally lead to the absence of quasiparticles. The resulting correlated quantum fluid, when thermally excited, displays rich universal dyn…
Structure of the third moment of the generalized Rosenblatt distribution
Shuyang Bai, Murad S. Taqqu
The Rosenblatt distribution appears as limit in non-central limit theorems. The generalized Rosenblatt distribution is obtained by allowing different power exponents in the kernel…
The impact of the diagonals of polynomial forms on limit theorems with long memory
Shuyang Bai, Murad S. Taqqu
We start with an i.i.d. sequence and consider the product of two polynomial-forms moving averages based on that sequence. The coefficients of the polynomial forms are asymptoticall…
Convergence of long-memory discrete -th order Volterra processes
Shuyang Bai, Murad S. Taqqu
We obtain limit theorems for a class of nonlinear discrete-time processes called the -th order Volterra processes of order . These are moving average -th order poly…
Generalized Hermite processes, discrete chaos and limit theorems
Shuyang Bai, Murad S. Taqqu
We introduce a broad class of self-similar processes called generalized Hermite process. They have stationary increments, are defined on a Wiener chaos with Hurst…
Multivariate limits of multilinear polynomial-form processes with long memory
Murad S. Taqqu, Shuyang Bai
We consider the multilinear polynomial-form process \[X(n)=\sum_{1\le i_1<\ldots<i_k<\infty}a_{i_1}\ldots a_{i_k}ε_{n-i_1}\ldotsε_{n-i_k},\] obtained by applying a multilinear poly…
Multivariate limit theorems in the context of long-range dependence
Murad S. Taqqu, Shuyang Bai
We study the limit law of a vector made up of normalized sums of functions of long-range dependent stationary Gaussian series. Depending on the memory parameter of the Gaussian ser…