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Hongshuai Dai

Publications and source records attributed to Hongshuai Dai.

14 recordsLinked to original sources
arXiv2019

Multidimensional Sticky Brownian Motions: Tail Behaviour of the Joint Stationary Distribution

Sticky Brownian motions, as time-changed semimartingale reflecting Brownian motions, have various applications in many fields, including queuing theory and mathematical finance. In this paper, we are concerned about the stationary distributions of a multidimensional sticky Brownian motion, provided it is stable. We will study the large deviations principle for stationary distribution and the tail behaviour of the joint stationary distribution.

math.PR↗
arXiv2018

Exact tail asymptotics for a three dimensional Brownian-driven tandem queue with intermediate inputs

The semimartingale reflecting Brownian motion (SRBM) can be a heavy traffic limit for many server queueing networks. Asymptotic properties for stationary probabilities of the SRBM have attracted a lot of attention recently. However, many results are obtained only for the two-dimensional SRBM. There is only little work related to higher dimensional ($\geq 3$) SRBMs. In this paper, we consider a three dimensional SRBM: A three dimensional Brownian-driven tandem queue with intermediate inputs. We are interested in tail asymptotics for stationary distributions. By generalizing the kernel method and using copula, we obtain exact tail asymptotics for the marginal stationary distribution of the buffer content in the third buffer and the joint stationary distribution.

math.PR↗
arXiv2018

Limit theorems for functionals of Gaussian vectors

Operator self-similar processes, as an extension of self-similar processes, have been studied extensively. In this work, we study limit theorems for functionals of Gaussian vectors. Under some conditions, we determine that the limit of partial sums of functionals of a stationary Gaussian sequence of random vectors is an operator self-similar process

math.PR↗
arXiv2018

Stationary Distributions for Two-Dimensional Sticky Brownian Motions: Exact Tail Asymptotics and Extreme Value Distributions

In this paper, we consider a two-dimensional sticky Brownian motion. Sticky Brownian motions can be viewed as time-changed semimartingale reflecting Brownian motions, which find applications in many areas including queueing theory and mathematical finance. For example, a sticky Brownian motion can be used to model a storage system.with exceptional services. In this paper, we focus on stationary distributions for sticky Brownian motions. The main results obtained here include tail asymptotic properties in boundary stationary distributions, marginal distributions, and joint distributions. The kernel method, copula concept and extreme value theory are main tools used in our analysis.

math.PR↗
arXiv2018

Operator Fractional Brownian Sheet and Martingale Differences

In this paper, inspired by the fractional Brownian sheet of Riemann-Liouville type, we introduce the operator fractional Brownian sheet of Riemman-Liouville type, and study some properties of it. We also present an approximation in law to it based on the martingale differences.

math.PR↗
arXiv2015

Convergence rates in precise asymptotics for a kind of complete moment convergence

In Liu and Lin (Statist. Probab. Letters, 2006), they introduced a kind of complete moment convergence which includes complete convergence as a special case. Inspired by the study of complete convergence, in this paper, we study the convergence rates of the precise asymptotics for this kind of complete moment convergence and get the corresponding convergence rates.

math.PR↗
arXiv2015

Adaptive Elastic Net Method for Cox Model

In this paper, we study the Adaptive Elastic Net method for the Cox model. We prove the grouping effect and oracle property of its estimators. Finally, we show these two properties by an empirical analysis and a numerical simulation, respectively.

math.ST↗
arXiv2015

Elastic Net Procedure for Partially Linear Models

Variable selection plays an important role in the high-dimensional data analysis. However the high-dimensional data often induces the strongly correlated variables problem. In this paper, we propose Elastic Net procedure for partially linear models and prove the group effect of its estimate. By a simulation study, we show that the strongly correlated variables problem can be better handled by the Elastic Net procedure than Lasso, ALasso and Ridge. Based on an empirical analysis, we can get that the Elastic Net procedure is particularly useful when the number of predictors $p$ is much bigger than the sample size $n$.

stat.ME↗
arXiv2014

Exact tail asymptotics for a discrete-time preemptive priority queue

In this paper, we consider a discrete-time preemptive priority queue with different service rates for two classes of customers, one with high-priority and the other with low-priority. This model corresponds to the classical preemptive priority queueing system with two classes of independent Poisson customers and a single exponential server. Due to the possibility of customers' arriving and departing at the same time in a discrete-time queue, the model considered in this paper is more complicated. In this model, we focus on the characterization of exact tail asymptotics for the joint stationary distribution of the queue length of the two classes of customers, for the two boundary distributions and for the two marginal distributions, respectively. By using generating functions and kernel method, we get an explicit expression of exact tail asymptotics along the low-priority queue direction, as well as along the high-priority queue direction.

math.PR↗
arXiv2014

Random Walks and Subfractional Brownian Motion

In this article, we show a result of approximation in law to subfractional Brownian motion, with $H>\frac{1}{2}$, in the Skorohod topology. The construction of these approximations is based on a sequence of I.I.D random variables

math.PR↗
arXiv2013

Operator Fractional Brownian Motion and Martingale Differences

It is well known that martingale difference sequences are very useful in applications and theory. On the other hand, the operator fractional Brownian motion as an extension of the well-known fractional Brownian motion also plays important role in both applications and theory. In this paper, we study the relationship between them. We will construct an approximation sequence of operator fractional Brownian motion based on a martingale difference sequence.

math.PR↗
arXiv2012

Approximation to multifractional Riemann-Liouville Brownian sheet

In this paper, we first introduce multifrational Riemann-Liouville Brownian sheets. Then, we show a result of approximation in law of the multifractional Riemann-Liouville Brownian sheet. The construction of these approximations is based on a sequence of I.I.D random variables.

math.PR↗
arXiv2012

Approximations of fractional Brownian motion

Approximations of fractional Brownian motion using Poisson processes whose parameter sets have the same dimensions as the approximated processes have been studied in the literature. In this paper, a special approximation to the one-parameter fractional Brownian motion is constructed using a two-parameter Poisson process. The proof involves the tightness and identification of finite-dimensional distributions.

math.ST↗