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Distribution Function of the Blow up Time of the Solution of an Anticipating Random Fatigue Equation

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Acta Mathematica Sinica,English Series 2021年第4期37卷 551-564页

作者： Liliana PERALTA Centro de Investigacion en Matematicas UAEHCarretera Pachuca-Tulancingo km 4.5 PachucaHidalgo 42184Mexico

In this paper,we study the distribution function of the time of explosion of a stochastic differential equation modeling the length of the dominant crack due to *** main novelty is that initial condition is regarded as an anticipating random variable and the stochastic integral is in the forward *** suitable conditions,we use the substitution formula from Russo and Vallois to find the local solution of this ***,we find the law of blow up time by proving some results on barrier crossing probabilities of brownian bridge.

关键词： Stochastic differential equations random fatigue explosion time forward integral brownian bridge

The CUSUM statistic of change point under NA sequences

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Applied Mathematics(A Journal of Chinese Universities) 2021年第4期36卷 512-520页

作者： LING Jin LI Xiao-qin YANG Wen-zhi JIAO Jian-ling School of Management Hefei University of TechnologyHefei 230009China Center for Applied Mathematics School of Mathematical SciencesAnhui UniversityHefei 230061China

In this paper,we investigate the CUSUM statistic of change point under the neg-atively associated(NA)*** establishing the consistency estimators for mean and covariance functions respectively,the limit distribution of the CUSUM statistic is proved to be a standard brownian bridge,which extends the results obtained under the case of an indepen-dent normal sample and the moving average ***,the finite sample properties of the CUSUM statistic are given to show the efficiency of the method by simulation studies and an application on a real data analysis.

关键词： CUSUM statistic limit distribution NA sequences brownian bridge

A General Law of Moment Convergence Rates for Uniform Empirical Process

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Acta Mathematica Sinica,English Series 2011年第10期27卷 1941-1948页

作者： Qing Pei ZANG School of Mathematical Science Huaiyin Normal UniversityHuai'an 223300 P. R. China

Let {Xn; n ≥ 1} be a sequence of independent and identically distributed U[0,1]-distributed random variables. Define the uniform empirical process Fn（t） = n^-1/2 ∑^ni=1 （I{xi≤t} - t）, 0 ≤ t 〈 1, ││Fn││ = sup0≤t≤ 1 │Fn（t）│. In this paper, the exact convergence rates of a general law of weighted infinite series of E{││Fn││ -εg^s（n）}＋ are obtained.

关键词： Moment convergence rates uniform empirical process brownian bridge

Test for autocorrelation change in discretely observed Ornstein-Uhlenbeck processes driven by Lévy processes

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Science China Mathematics 2013年第2期56卷 339-357页

作者： ZHANG ShiBin ZHANG XinSheng Department of Mathematics Shanghai Maritime University Department of Statistics Fudan University

In this paper, we consider the problem of testing for an autocorrelation change in discretely observed Ornstein-Uhlenbeck processes driven by Levy processes. For a test, we propose a class of test statistics constructed by an iterated cumulative sums of squares of the difference between two adjacent observations. It is shown that each of the test statistics weakly converges to the supremum of the square of a brownian bridge. The test statistics are evaluated by some empirical results.

关键词： autocorrelation brownian bridge cusum test Ornstein-Uhlenbeck test for parameter change,weak convergence

Modified Testing for Structural Changes in Autoregressive Processes

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Journal of Mathematical Research and Exposition 2011年第1期31卷 79-90页

作者： Hao JIN Zheng TIAN Yun Feng YANG School of Science Xi'an University of Science and Technology Shaanxi 710054 P. R. China Department of Applied Mathematics Northwestern Polytechnical University Shaanxi 710072 P. R. China State Key Laboratory of Remote Sensing Science Chinese Academy of Sciences Beijing 100101 P. R. China

In this paper, we consider the problem of detecting for structural changes in the autoregressive processes including AR（p） process. In performing a test, we employ the conventional residual CUSUM of squares test （RCUSQ） statistic. The RCUSQ test is based on the subsampling method introduced by Jach and Kokoszka [J. Methodology and Computing in Applied Probability 25（2004）]. It is shown that under regularity conditions, the asymptotic distribution of the test statistic is the function of a standard brownian bridge. Simulation results as to AR（1） process and an example of real data analysis are provided for illustration.

关键词： subsampling RCUSQ test brownian bridge structural changes

Variational Approach for the Adapted Solution of Backw ard Stochastic Differential Equations with Locally Lipschitz Diffusion Coefficients

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Journal of Donghua University(English Edition) 2012年第4期29卷 341-350页

作者：谢臻赟刘奕 Department of Applied Mathematics Donghua University College of Humanities Donghua University

One existence integral condition was obtained for the adapted solution of the general backward stochastic differential equations(BSDEs). Then by solving the integral constraint condition, and using a limit procedure, a new approach method is proposed and the existence of the solution was proved for the BSDEs if the diffusion coefficients satisfy the locally Lipschitz condition. In the special case the solution was a brownian bridge. The uniqueness is also considered in the meaning of "F0-integrable equivalent class" . The new approach method would give us an efficient way to control the main object instead of the "noise".

关键词： backward stochastic differential equation (BSDE) variational approach locally Lipschitz condition existence Fointegrable equivalent class uniqueness brownian bridge

Residual Cusum Test for Parameters Change in ARCH Errors Models with Deterministic Trend

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Journal of Mathematical Research and Exposition 2009年第6期29卷 1011-1021页

作者：金浩田铮 Department of Applied Mathematics Northwestern Polytechnical University State Key Laboratory of Remote Sensing Science Chinese Academy of Science

This paper analyzes the problem of testing for parameters change in ARCH errors models with deterministic trend based on residual cusum test. It is shown that the asymptotically limiting distribution of the residual cusum test statistic is still the sup of a standard brownian bridge under null hypothesis. In order to check this, we carry out a Monte Carlo simulation and examine the return of IBM data. The results from both simulation and real data analysis support our claim. We also can explain this phenomenon from a theoretical viewpoint that the variance in ARCH model in mainly determined by its parameters.

关键词： residual cusum test invariance principle brownian bridge change point.

Tests for Parameter Changes in Time Series

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Chinese Quarterly Journal of Mathematics 2011年第1期26卷 120-124页

作者： JIN Hao YANG Yun-feng School of Science Xi＇an University of Science and TechnologyXi＇an 710054China Mining Engineering Post-doctoral Xi＇an University of Science and TechnologyXi＇an 710054China

The paper considers the problem of testing for a change point in the parameters of AR（p） *** is shown that the asymptotically limiting distribution of the residual CUSUM of squares test（RCUSQ） is still the sup of a standard brownian bridge under null *** also show via simulations that our asymptotic results provide good approximations in finite samples.

关键词： change point brownian bridge RCUSQ test