Peng Liu

activity

20152021

most citedDrawdown and drawup for fractional Brownian motion with trend

2 citations · 3 across the 5 of their papers we have counts for

collaborators

9 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

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…