摘要：
在水位流量关系曲线拟合中,非线性最小二乘法( Non-linear Least Square,NLS)是广泛运用的方法。但NLS中采用的对数变换有时不能起到稳定方差的作用,且没有考虑异方差会导致水位流量关系中的参数和流量估计值不可靠的问题。为了克服这个局限性,采用Box-Cox变换进行改进,并利用极大似然估计法( Maximum Likelihood Estimation,MLE)对变换后的模型进行参数估计。结果表明:相比于NLS中的对数变换模型,基于Box-Cox变换模型能更好地得到稳定方差,更倾向产生正态分布。并且发现对数变换模型是Box-Cox变换模型的一个特例,因此Box-Cox变换模型能够更合理地推断水位流量关系,在实际应用中的适用范围更广。
摘要：
For diffusion processes, we extend various two-sided exit identities to the situation when the process is only observed at arrival times of an independent Poisson process. The results are expressed in terms of solutions to the differential equations associated with the diffusions generators.
作者机构：
[Liu, Wei] Hunan Univ Finance & Econ, Coll Math & Stat, Changsha 410205, Peoples R China.;[Li, Ying Qiu] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Peoples R China.
通讯机构：
[Liu, Wei] H;Hunan Univ Finance & Econ, Coll Math & Stat, Changsha 410205, Peoples R China.
关键词：
High-dimensional data;maximum type test;sign-based dense test;sign-based sparsity test;sum of squares type test;testing mean vector
摘要：
In this article, we introduce a robust sparse test statistic which is based on the maximum type statistic. Both the limiting null distribution of the test statistic and the power of the test are analysed. It is shown that the test is particularly powerful against sparse alternatives. Numerical studies are carried out to examine the numerical performance of the test and to compare it with other tests available in the literature. The numerical results show that the test proposed significantly outperforms those tests in a range of settings, especially for sparse alternatives.
通讯机构：
[Liu, Quansheng] U;Univ Bretagne Sud, UMR 6205, LMBA, F-56000 Vannes, France.
关键词：
Mandelbrot's cascade;Branching random walk;Random environment;Harmonic moments;Large deviations;Moderate deviations
摘要：
For Mandelbrot's cascade in a random environment, we find the critical value for the existence of harmonic moments of the limit variable of Mandelbrot's martingale, and establish large and moderate deviation principles for the free energy. As applications, we show the corresponding limit theorems for branching random walks in random environments. (C) 2018 Elsevier B.V. All rights reserved.
作者机构：
[李应求; 安勃] School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha;410114, China;[李恒通] Faculty of Science, National University of Singapore, Kent Ridge;119077, Singapore;[李应求; 安勃] 410114, China
通讯机构：
[Li, Y.] S;School of Mathematics and Statistics, China
作者机构：
[Wang, Yuejiao] Hunan First Normal Univ, Coll Math & Computat Sci, Changsha 410205, Hunan, Peoples R China.;[Liu, Zaiming] Cent South Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China.;[Liu, Quansheng] Univ Bretagne Sud, LMBA, UMR CNRS 6205, F-56000 Vannes, France.;[Li, Yingqiu; Liu, Quansheng] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 41004, Hunan, Peoples R China.
通讯机构：
[Liu, Quansheng] U;[Liu, Quansheng] C;Univ Bretagne Sud, LMBA, UMR CNRS 6205, F-56000 Vannes, France.;Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 41004, Hunan, Peoples R China.
关键词：
branching random walk;random environment;quenched moments;weighted moments
摘要：
We consider a branching random walk in an independent and identically distributed random environment ξ = (ξn) indexed by the time. Let W be the limit of the martingale
$$W_n=\int\;e^{-tx}Z_n(\text{d}x)/\mathbb{E}_\xi\int\;e^{-tx}Z_n(\text{d}x)$$
, with Zn denoting the counting measure of particles of generation n, and
$$\mathbb{E}_\xi$$
the conditional expectation given the environment ξ. We find necessary and sufficient conditions for the existence of quenched moments and weighted moments of W, when W is non-degenerate.
关键词：
long span bridge;vehicle load;extreme value distribution;the Extended Burr XII distribution;Bayesian estimation;Markov chain Monte Carlo simulation
作者机构：
[李应求; 彭雪莲] School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, 410114, China;[李德如] School of Civil Engineering and Architecture, Changsha University of Science and Technology, Changsha, 410114, China;[潘生] School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, 200433, China
期刊：
Statistics & Probability Letters,2017年127:97-103 ISSN：0167-7152
通讯作者：
Liu, Quansheng
作者机构：
[Wang, Yuejiao; Liu, Zaiming] Cent South Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China.;[Li, Yingqiu; Liu, Quansheng] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410004, Hunan, Peoples R China.;[Liu, Quansheng] Univ Bretagne Sud, UMR 6205, LMBA, F-56000 Vannes, France.
通讯机构：
[Liu, Quansheng] U;Univ Bretagne Sud, UMR 6205, LMBA, F-56000 Vannes, France.
关键词：
Branching process;Random environment;Concept of subcriticality and criticality;Convergence rate of survival probability;Ratio theorem
摘要：
We consider a branching process (Z(n)) in a stationary and ergodic random environment xi = (xi(n)). Athreya and Karlin (1971) proved the basic result about the concept of subcriticality and criticality, by showing that under the quenched law P-xi , the conditional distribution of Z(n) given the non-extinction at time n converges in law to a proper distribution on N+ = {1, 2,. . .} in the subcritical case, and to the null distribution in the critical case, under the condition that the environment sequence is exchangeable. In this paper we first improve this basic result by removing the exchangeability condition on the environment, and by establishing a more general result about the conditional law of Z(n) given the non extinction at time n + k for each fixed k >= 0. As a by-product of the proof we also remove the exchangeability condition in another result of Athreya and Karlin (1971) for the subcritical case about the decay rate of the survival probability given the environment. We then establish a convergence theorem about the ratio P-xi (Z(n) = j)/P-xi(Z(n) = 1), which can be applicable in each of the subcritical, critical, and supercritical cases. (C) 2017 Elsevier B.V. All rights reserved.
摘要：
For a < r < b, the approach of Li and Zhou (2014) is adopted to find joint Laplace transforms of occupation times over intervals (a, r) and (r, b) for a time homogeneous diffusion process before it first exits from either a or b. The results are expressed in terms of solutions to the differential equations associated with the diffusions generator. Applying these results, we obtain more explicit expressions on the joint Laplace transforms of occupation times for Brownian motion with drift, Brownian motion with alternating drift and skew Brownian motion, respectively.
关键词：
Joint occupation time;Laplace transform;Potential measure;Spectrally negative Lévy process
摘要：
For spectrally negative Levy processes, we find expressions of potential measures that are discounted by their joint occupation times over semi-infinite intervals (-infinity, 0) and (0, infinity). These expressions are in terms of the associated scale functions and the inverse functions of Laplace exponents. (C) 2015 Elsevier B.V. All rights reserved.
期刊：
Statistics & Probability Letters,2015年100:12-18 ISSN：0167-7152
通讯作者：
Liu, Wei
作者机构：
[Liu, Wei; Ma, Chaoqun] Hunan Univ, Sch Business, Changsha 410082, Hunan, Peoples R China.;[Li, Yingqiu] Changsha Univ Sci & Technol, Coll Math & Comp Sci, Changsha 410114, Hunan, Peoples R China.;[Wang, Suming] Dongguan Univ Technol, City Coll, Dept Comp & Informat Sci, Dongguan 523106, Peoples R China.;[Liu, Wei] Hunan Univ, Sch Business, Room A-404,11 South Lushan Rd, Changsha 410082, Hunan, Peoples R China.
通讯机构：
[Liu, Wei] H;Hunan Univ, Sch Business, Room A-404,11 South Lushan Rd, Changsha 410082, Hunan, Peoples R China.
关键词：
Bi-infinite random environment;Markov chain;Strong limit;Conditional relative entropy density
摘要：
We consider strong limit theorems for Markov chains in bi-infinite random environments. We first give a new proof of a strong limit theorem of Liu and Yang (1995) on the average of functions of non-homogeneous Markov chains by constructing a nonnegative martingale. As corollaries, for a Markov chain in a bi-infinite random environment, we obtain strong limit theorems for the conditional relative entropy and for the number of times that the Markov chain and related processes reach a given point. (C) 2015 Elsevier B.V. All rights reserved.
期刊：
Advances in Computer Science Research,2015年18:738-741 ISSN：2352-538X
通讯作者：
Chen, F. Y.
作者机构：
[Chen, F. Y.; Tan, Y. Y.] Insurance Profess Coll, Changsha, Hunan, Peoples R China.;[Li, Y. Q.] Changsha Univ Sci & Technol, Sch Math & Computat Sci, Changsha, Hunan, Peoples R China.
通讯机构：
[Chen, F. Y.] I;Insurance Profess Coll, Changsha, Hunan, Peoples R China.
会议名称：
2015 International Conference on Computer Information Systems and Industrial Applications(CISIA2015)
会议时间：
2015-06-28
会议地点：
泰国曼谷
关键词：
warrant bonds;fractional brownian motion;option;risk-neutral pricing theory
摘要：
Assuming that the underlying stock follows Fractional Brownian motion and that stochastic interest rate meets the Vasicek model of interest rates, this paper establishes pricing model of Warrant Bonds and deduces the pricing formula of Warrant Bonds by utilizing risk-neutral valuation theory. Finally, this paper analyzes influence of concerned parameters of pricing model on the value of Warrant Bonds by using the numerical simulations.
