Peng Liu

activity

20142021

most citedSojourn times of Gaussian processes with trend

21 citations · 59 across the 19 of their papers we have counts for

collaborators

19 papers

math.PR2021

Sojourn times of Gaussian related random fields

Krzysztof Dȩbicki, Enkelejd Hashorva, Peng Liu +1

This paper is concerned with the asymptotic analysis of sojourn times of random fields with continuous sample paths. Under a very general framework we show that there is an interes…

math.PR2018★ 21 cited

Sojourn times of Gaussian processes with trend

Krzysztof Debicki, Peng Liu, Zbigniew Michna

We derive exact tail asymptotics of sojourn time above the level $u \geq 0$ $P (v (u) \int_{0}^{T} I (X (t) - c t > u) d t > x), x \geq 0$ as $u \to \infty$ , wher…

math.PR2018

Ruin problem for Brownian motion risk model with interest rate and tax payment

Long Bai, Peng Liu

Let ${B (t), t \geq 0}$ be a Brownian motion. Consider the Brownian motion risk model with interest rate collection and tax payment defined by \begin{align}\label{Rudef} \widetilde{…

math.PR2018

Extremes of Spherical Fractional Brownian Motion

Dan Cheng, Peng Liu

Let ${B_{β} (x), x \in S^{N}}$ be a fractional Brownian motion on the $N$ -dimensional unit sphere $S^{N}$ with Hurst index $β$ . We study the excursion probability $\ma…

math.PR2018★ 2 cited

Drawdown and drawup for fractional Brownian motion with trend

Long Bai, Peng Liu

In this paper, we consider the drawdown and drawup of the fractional Brownian motion with trend, which corresponds to the logarithm of geometric fractional Brownian motion represen…

math.PR2018

The time of ultimate recovery in Gaussian risk model

Krzysztof Debicki, Peng Liu

We analyze the distance $R_{T} (u)$ between the first and the last passage time of ${X (t) - c t : t \in [0, T]}$ at level $u$ in time horizon $T \in (0, \infty]$ , where $X$ is a cen…

math.PR2018

Extremes of vector-valued Gaussian processes with Trend

Long Bai, Krzysztof Debicki, Peng Liu

Let $X (t) = (X_{1} (t), \dots, X_{n} (t)), t \in T \subset R$ be a centered vector-valued Gaussian process with independent components and continuous trajectories, and $h…

math.PR2018

Tail Asymptotic Behavior of the supremum of a class of chi-square processes

Lanpeng Ji, Peng Liu, Stephan Robert

In this paper, we analyze a multivariate counterpart of the generalized weighted Kolmogorov-Smirnov statistic, which is the supremum of weighted locally stationary chi-square proce…

math.PR2017★ 1 cited

Sample path properties of reflected Gaussian processes

Kamil Marcin Kosiński, Peng Liu

We consider a stationary queueing process $Q_{X}$ fed by a centered Gaussian process $X$ with stationary increments and variance function satisfying classical regularity conditions.…

math.PR2017★ 1 cited

Extremes of nonstationary Gaussian fluid queues

Krzysztof Debicki, Peng Liu

This contribution investigates asymptotic properties of transient queue length process $$ Q(t)=\max\left(x+X(t)-ct, \sup_{0\leq s\leq t}\left(X(t)-X(s)-c(t-s)\right)\right),\ \ \ t…

math.PR2016★ 3 cited

Extremes of Gaussian Random Fields with maximum variance attained over smooth curves

Peng Liu

Let $X (s, t), (s, t) \in E$ , with $E \subset R^{2}$ a compact set, be a centered two dimensional Gaussian random field with continuous trajectories and variance function $σ(s,t)…

math.PR2016

A note on ruin problems in perturbed classical risk models

Peng Liu, Chunsheng Zhang, Lanpeng Ji

In this short note, we derive explicit formulas for the joint densities of the time to ruin and the number of claims until ruin in perturbed classical risk models, by constructing…

math.PR2016★ 5 cited

Uniform tail approximation of homogenous functionals of Gaussian fields

Krzysztof Dȩbicki, Enkelejd Hashorva, Peng Liu

Let $X (t), t \in R^{d}$ be a centered Gaussian random field with continuous trajectories and set $ξ_{u} (t) = X (f (u) t), t \in R^{d}$ with $f$ some positive function. Classical results establis…

math.PR2016★ 1 cited

Extremes of Gaussian Random Fields with regularly varying dependence structure

Krzyztof Dębicki, Enkelejd Hashorva, Peng Liu

Let $X (t), t \in T$ be a centered Gaussian random field with variance function $σ^{2} (\cdot)$ that attains its maximum at the unique point $t_{0} \in T$ , and let $M(\…

math.PR2015★ 3 cited

Extremes of $γ$ -reflected Gaussian process with stationary increments

Krzysztof Debicki, Enkelejd Hashorva, Peng Liu

For a given centered Gaussian process with stationary increments ${X (t), t \geq 0}$ and $c > 0$ , let $W_{γ} (t) = X (t) - c t - γ 0 \leq s \leq t in f (X (s) - cs), t \geq 0$ den…

math.PR2015★ 1 cited

Extremes of stationary Gasussian storage models

Krzysztof Dȩbicki, Peng Liu

For the stationary storage process ${Q (t), t \geq 0}$ , with $Q (t) = sup_{s \geq t} (X (s) - X (t) - c (s - t)^{β}),$ where ${X (t), t \geq 0}$ is a centered Gaussian process with stat…

math.PR2015★ 17 cited

Extremes of locally stationary chi-square processes with trend

Peng Liu, Lanpeng Ji

Chi-square processes with trend appear naturally as limiting processes in various statistical models. In this paper we are concerned with the exact tail asymptotics of the supremum…

math.PR2014★ 4 cited

Extremes of Chi-square Processes with Trend

Peng Liu, Lanpeng Ji

This paper studies the supremum of a chi-square process with trend over a threshold-dependent-time horizon. Under the assumption that the chi-square process is generated from a cen…

math.PR2014

On the gamma-reflected processes with fBm input

Peng Liu, Enkelejd Hashorva, Lanpeng Ji

Define a $γ$ -reflected process $W_{γ} (t) = Y_{H} (t) - γ in f_{s \in [0, t]} Y_{H} (s)$ , $t \geq 0$ with input process ${Y_{H} (t), t \geq 0}$ which is a fractional Brownian motion with Hurst index $H\in…

Sojourn times of Gaussian related random fields

Sojourn times of Gaussian processes with trend

Ruin problem for Brownian motion risk model with interest rate and tax payment

Extremes of Spherical Fractional Brownian Motion

Drawdown and drawup for fractional Brownian motion with trend

The time of ultimate recovery in Gaussian risk model

Extremes of vector-valued Gaussian processes with Trend

Tail Asymptotic Behavior of the supremum of a class of chi-square processes

Sample path properties of reflected Gaussian processes

Extremes of nonstationary Gaussian fluid queues

Extremes of Gaussian Random Fields with maximum variance attained over smooth curves

A note on ruin problems in perturbed classical risk models

Uniform tail approximation of homogenous functionals of Gaussian fields

Extremes of Gaussian Random Fields with regularly varying dependence structure

Extremes of γ-reflected Gaussian process with stationary increments

Extremes of stationary Gasussian storage models

Extremes of locally stationary chi-square processes with trend

Extremes of Chi-square Processes with Trend

On the gamma-reflected processes with fBm input

Extremes of $γ$ -reflected Gaussian process with stationary increments