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

Showing 2018Show all

7 papers · 1 filter

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…