Author
Lanpeng Ji
Other affiliations: Nankai University, University of Leeds
Bio: Lanpeng Ji is an academic researcher from University of Lausanne. The author has contributed to research in topics: Fractional Brownian motion & Gaussian. The author has an hindex of 17, co-authored 62 publications receiving 748 citations. Previous affiliations of Lanpeng Ji include Nankai University & University of Leeds.
Papers
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TL;DR: In this article, the exact tail asymptotic behavior of a fractional Brownian motion with Hurst index H ∈ ( 0, 1 ) with respect to the supremum of a mean-zero Gaussian random field is established.
49 citations
TL;DR: In this paper, the authors derived the asymptotics of finite-time ruin probability of time-changed fractional Brownian motion risk processes with respect to a non-negative constant.
Abstract: Let {X(t),t ≥ 0} be a centered Gaussian process and let γ be a non-negative constant. In this paper we study the asymptotics of $\mathbb {P} \left \{\underset {t\in [0,\mathcal {T}/u^{\gamma }]}\sup X(t)>u\right \}$
as $u\rightarrow \infty $
, with $\mathcal {T}$
an independent of X non-negative random variable. As an application, we derive the asymptotics of finite-time ruin probability of time-changed fractional Brownian motion risk processes.
46 citations
TL;DR: The Piterbarg theorems for chi-processes with trend were derived in this article for both stationary and non-stationary Gaussian processes with constant degrees of freedom.
Abstract: Let \(\chi _{n}(t) = ({\sum }_{i=1}^{n} {X_{i}^{2}}(t))^{1/2},\ {t\ge 0}\) be a chi-process with n degrees of freedom where X i ’s are independent copies of some generic centered Gaussian process X. This paper derives the exact asymptotic behaviour of
$$ \mathbb{P}\left\{\sup\limits_{t\in[0,T]} \left(\chi_{n}(t)- {g(t)} \right) > u\right\} \;\; \text{as} \;\; u \rightarrow \infty, $$
(1)
where T is a given positive constant, and g(⋅) is some non-negative bounded measurable function. The case g(t)≡0 has been investigated in numerous contributions by V.I. Piterbarg. Our novel asymptotic results, for both stationary and non-stationary X, are referred to as Piterbarg theorems for chi-processes with trend.
42 citations
TL;DR: In this paper, the exact asymptotics of P ( ∃ t ∈ [ 0, T ] ∀ i = 1, …, n X i ( t ) > u ) as u → ∞, for both locally stationary X i and X i ) with a non-constant generalized variance function were derived.
41 citations
TL;DR: In this paper, the authors derived the exact asymptotics of the probability of Parisian ruin for self-similar Gaussian risk processes and derived the normal approximation of the Parisian time.
Abstract: In this paper we derive the exact asymptotics of the probability of Parisian ruin for self-similar Gaussian risk processes. Additionally, we obtain the normal approximation of the Parisian ruin time and derive an asymptotic relation between the Parisian and the classical ruin times.
39 citations
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2,345 citations
Book•
01 Jan 2013
TL;DR: In this paper, the authors consider the distributional properties of Levy processes and propose a potential theory for Levy processes, which is based on the Wiener-Hopf factorization.
Abstract: Preface to the revised edition Remarks on notation 1. Basic examples 2. Characterization and existence 3. Stable processes and their extensions 4. The Levy-Ito decomposition of sample functions 5. Distributional properties of Levy processes 6. Subordination and density transformation 7. Recurrence and transience 8. Potential theory for Levy processes 9. Wiener-Hopf factorizations 10. More distributional properties Supplement Solutions to exercises References and author index Subject index.
1,957 citations
TL;DR: In this paper, applied probability and queuing in the field of applied probabilistic analysis is discussed. But the authors focus on the application of queueing in the context of road traffic.
Abstract: (1987). Applied Probability and Queues. Journal of the Operational Research Society: Vol. 38, No. 11, pp. 1095-1096.
1,121 citations
01 Jan 2005
TL;DR: In this paper, the authors present a unified approach to the analysis of several popular models in collective risk theory, including the classical compound Poisson model, Sparre Andersen models with phase-type interclaim times and models with causal dependence of a certain Markovian type between claim sizes and inter claim times.
Abstract: We present a unified approach to the analysis of several popular models in collective risk theory. Based on the analysis of the discounted penalty function in a semi-Markovian risk model by means of Laplace–Stieltjes transforms, we rederive and extend some recent results in the field. In particular, the classical compound Poisson model, Sparre Andersen models with phase-type interclaim times and models with causal dependence of a certain Markovian type between claim sizes and interclaim times are contained as special cases.
105 citations