Spatial linear features are often represented as a series of line segments joined by measured endpoints in surveying and geographic information science.There are not only the measuring errors of the endpoints but also...Spatial linear features are often represented as a series of line segments joined by measured endpoints in surveying and geographic information science.There are not only the measuring errors of the endpoints but also the modeling errors between the line segments and the actual geographical features.This paper presents a Brownian bridge error model for line segments combining both the modeling and measuring errors.First,the Brownian bridge is used to establish the position distribution of the actual geographic feature represented by the line segment.Second,an error propagation model with the constraints of the measuring error distribution of the endpoints is proposed.Third,a comprehensive error band of the line segment is constructed,wherein both the modeling and measuring errors are contained.The proposed error model can be used to evaluate line segments’overall accuracy and trustability influenced by modeling and measuring errors,and provides a comprehensive quality indicator for the geospatial data.展开更多
In this paper,we investigate the CUSUM statistic of change point under the neg-atively associated(NA)sequences.By establishing the consistency estimators for mean and covariance functions respectively,the limit distri...In this paper,we investigate the CUSUM statistic of change point under the neg-atively associated(NA)sequences.By 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 processes.Finally,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.展开更多
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, ...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".展开更多
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 fatigue.The main novelty is that initial condition is re...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 fatigue.The main novelty is that initial condition is regarded as an anticipating random variable and the stochastic integral is in the forward sense.Under suitable conditions,we use the substitution formula from Russo and Vallois to find the local solution of this equation.Then,we find the law of blow up time by proving some results on barrier crossing probabilities of Brownian bridge.展开更多
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││ = ...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.展开更多
This paper provides sufficient conditions for the time of bankruptcy(of a company or a state)for being a totally inaccessible stopping time and provides the explicit computation of its compensator in a framework where...This paper provides sufficient conditions for the time of bankruptcy(of a company or a state)for being a totally inaccessible stopping time and provides the explicit computation of its compensator in a framework where the flow of market information on the default is modelled explicitly with a Brownian bridge between 0 and 0 on a random time interval.展开更多
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 (R...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.展开更多
基金National Natural Science Foundation of China(Nos.42071372,42221002)。
文摘Spatial linear features are often represented as a series of line segments joined by measured endpoints in surveying and geographic information science.There are not only the measuring errors of the endpoints but also the modeling errors between the line segments and the actual geographical features.This paper presents a Brownian bridge error model for line segments combining both the modeling and measuring errors.First,the Brownian bridge is used to establish the position distribution of the actual geographic feature represented by the line segment.Second,an error propagation model with the constraints of the measuring error distribution of the endpoints is proposed.Third,a comprehensive error band of the line segment is constructed,wherein both the modeling and measuring errors are contained.The proposed error model can be used to evaluate line segments’overall accuracy and trustability influenced by modeling and measuring errors,and provides a comprehensive quality indicator for the geospatial data.
基金Supported by the NNSF of China(11701004,11801003)NSSF of China(14ATJ005)+1 种基金NSF of Anhui Province(1808085QA03,1808085QA17,1808085QF212,2008085MA14)Provincial Natural Science Research Project of Anhui Colleges(KJ2019A0006,KJ2019A0021).
文摘In this paper,we investigate the CUSUM statistic of change point under the neg-atively associated(NA)sequences.By 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 processes.Finally,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.
基金National Natural Science Foundation of China ( No. 11171062 ) Natural Science Foundation for the Youth,China ( No.11101077) Innovation Program of Shanghai Municipal Education Commission,China ( No. 12ZZ063)
文摘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".
文摘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 fatigue.The main novelty is that initial condition is regarded as an anticipating random variable and the stochastic integral is in the forward sense.Under suitable conditions,we use the substitution formula from Russo and Vallois to find the local solution of this equation.Then,we find the law of blow up time by proving some results on barrier crossing probabilities of Brownian bridge.
基金Supported by National Natural Science Foundation of China (Grant No. 10901138), National Science Fundation of Zhejiang Province (Grant No. R6090034) and the Young Excellent Talent Foundation of Huaiyin Normal University Thanks are due to the referees for valuable comments that have led to improvements in this work.
文摘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.
基金supported by the European Community’s FP 7 Program under contract PITN-GA-2008-213841,and Marie Curie ITN《Controlled Systems》.
文摘This paper provides sufficient conditions for the time of bankruptcy(of a company or a state)for being a totally inaccessible stopping time and provides the explicit computation of its compensator in a framework where the flow of market information on the default is modelled explicitly with a Brownian bridge between 0 and 0 on a random time interval.
基金Supported by the National Natural Science Foundation of China (Grant Nos.7087309408&ZD046+1 种基金109261972010039)
文摘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.