Extremes on different grids and continuous time of stationary processes

Ling, Chengxiu; Peng, Zuoxiang; Tan, Zhongquan

doi:10.1016/j.jmaa.2018.01.008

Cited by 3 publications

(2 citation statements)

References 25 publications

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“…The recent contribution [3] discussed (1.1) and gave the approximations of the related sojourn time of discrete form for locally stationary Gaussian processes, and [4] investigated general Gaussian processes with strictly positive drift function. For more related discussions on ruin time and the extremal analysis of Gaussian processes and random fields in financial and insurance framework, we refer to [5][6][7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

On Generalized Berman Constants

Ling

Zhao

2019

Methodol Comput Appl Probab

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This paper aims to evaluate the Piterbarg-Berman function given bywith h a drift function and B α a fractional Brownian motion (fBm) with Hurst index α/2 ∈ (0, 1], i.e., a mean zero Gaussian process with continuous sample paths and covariance functionThis note specifies its explicit expression for the fBms with α = 1 and 2 when the drift function h(t) = ct α , c > 0 and E = R + ∪ {0}. For the Gaussian distribution B 2 , we investigate PB h 2 (x, E) with general drift function h(t) such that h(t) + t 2 being convex or concave, and finite interval E = [a, b].Typical examples of PB h 2 (x, E) with h(t) = c |t| λ − t 2 and several bounds of PB h α (x, E) are discussed. Numerical studies are carried out to illustrate all the findings.

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Section: Introductionmentioning

confidence: 99%

On Generalized Berman Constants

Ling

Zhao

2019

Methodol Comput Appl Probab

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“…Extending the above results to non-Gaussian case is also interesting, since most of reality can not be modeled by Gaussian model. Turkman (2012) considered this problem by adopting the model from Albin (1990), but there are some mistakes in the paper, which have been corrected by Ling et al (2017). Ling and Tan (2016) dealt with the problems for chi-processes.…”

Section: Introductionmentioning

confidence: 99%

On the maxima of continuous and discrete time Gaussian order statistics processes

Tan

2019

Preprint

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In this paper, we study the asymptotic relation between the maximum of a continuous order statistics process formed by stationary Gaussian processes and the maximum of this process sampled at discrete time points. It is shown that, these two maxima are asymptotically independent when the Gaussian processes are weakly dependent and the discrete points are sufficient sparse, while for other case, these two maxima are asymptotically dependent.

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