In this paper,we establish an invariance principle for ρ^--mixing random sequences under some moment condition.The result improve and extend the relevant result of Wu（2003）.
Statistics of exponentially decaying radiation of any nuclide always obeys the binomial stochastic distribution. The variance is derived for the number of atoms disintegrating in a time interval. The variance determin...Statistics of exponentially decaying radiation of any nuclide always obeys the binomial stochastic distribution. The variance is derived for the number of atoms disintegrating in a time interval. The variance determines the error of the disintegrations number. When the measuring time is short compared with the half life, then the Poisson stochastics is valid. Today, computers can be used to determine either distribution very easily. The dependence of absolute and relative error on the measuring time interval is examined, but here assuming the absence of the background contribution.展开更多
This paper investigates the controllability problem of time-variant linear stochastic controlsystems.A sufficient and necessary condition is established for stochastic exact controllability,whichprovides a useful alge...This paper investigates the controllability problem of time-variant linear stochastic controlsystems.A sufficient and necessary condition is established for stochastic exact controllability,whichprovides a useful algebraic criterion for stochastic control systems.Furthermore,when the stochasticsystems degenerate to deterministic systems,the algebraic criterion becomes the counterpart for thecomplete controllability of deterministic control systems.展开更多
We consider a class of stochastic Boussinesq equations driven by L6vy processes and establish the uniqueness of its invariant measure. The proof is based on the progressive stopping time technique.
In this paper we present an L2-theory for a class of stochastic partial differential equations driven by Levy processes. The coefficients of the equations are random functions depending on time and space variables, an...In this paper we present an L2-theory for a class of stochastic partial differential equations driven by Levy processes. The coefficients of the equations are random functions depending on time and space variables, and no smoothness assumption of the coefficients is assumed.展开更多
The classical chi-squared goodness of fit test assumes the number of classes is fixed,meanwhile the test statistic has a limiting chi-square distribution under the null hypothesis.It is well known that the number of c...The classical chi-squared goodness of fit test assumes the number of classes is fixed,meanwhile the test statistic has a limiting chi-square distribution under the null hypothesis.It is well known that the number of classes varying with sample size in the test has attached more and more attention.However,in this situation,there is not theoretical results for the asymptotic property of such chi-squared test statistic.This paper proves the consistency of chi-squared test with varying number of classes under some conditions.Meanwhile,the authors also give a convergence rate of KolmogorovSimirnov distance between the test statistic and corresponding chi-square distributed random variable.In addition,a real example and simulation results validate the reasonability of theoretical result and the superiority of chi-squared test with varying number of classes.展开更多
基金Supported by the National Natural Science Foundation of China（10661006） Supported by the New Century Guangxi Ten-hundred-thousand Talents Project（2005214）
文摘In this paper,we establish an invariance principle for ρ^--mixing random sequences under some moment condition.The result improve and extend the relevant result of Wu（2003）.
文摘Statistics of exponentially decaying radiation of any nuclide always obeys the binomial stochastic distribution. The variance is derived for the number of atoms disintegrating in a time interval. The variance determines the error of the disintegrations number. When the measuring time is short compared with the half life, then the Poisson stochastics is valid. Today, computers can be used to determine either distribution very easily. The dependence of absolute and relative error on the measuring time interval is examined, but here assuming the absence of the background contribution.
基金supported by the National Natural Science Foundation under Grant Nos.60904029 and 60704002the State Key Laboratory under Grant No.RCS2008ZT002
文摘This paper investigates the controllability problem of time-variant linear stochastic controlsystems.A sufficient and necessary condition is established for stochastic exact controllability,whichprovides a useful algebraic criterion for stochastic control systems.Furthermore,when the stochasticsystems degenerate to deterministic systems,the algebraic criterion becomes the counterpart for thecomplete controllability of deterministic control systems.
基金supported by National Natural Science Foundation of China (Grant Nos.10971225 and 11101427)Natural Science Foundation of Hunan Province (Grant No. 11JJ3004)the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State the Ministry of Education of China
文摘We consider a class of stochastic Boussinesq equations driven by L6vy processes and establish the uniqueness of its invariant measure. The proof is based on the progressive stopping time technique.
基金supported by National Science Foundation of US (Grant No. DMS-0906743)the National Research Foundation of Korea (Grant No. 20110027230)
文摘In this paper we present an L2-theory for a class of stochastic partial differential equations driven by Levy processes. The coefficients of the equations are random functions depending on time and space variables, and no smoothness assumption of the coefficients is assumed.
基金supported by the Natural Science Foundation of China under Grant Nos.11071022,11028103,11231010,11471223,BCMIISthe Beijing Municipal Educational Commission Foundation under Grant Nos.KZ201410028030,KM201210028005Jishou University Subject in 2014(No:14JD035)
文摘The classical chi-squared goodness of fit test assumes the number of classes is fixed,meanwhile the test statistic has a limiting chi-square distribution under the null hypothesis.It is well known that the number of classes varying with sample size in the test has attached more and more attention.However,in this situation,there is not theoretical results for the asymptotic property of such chi-squared test statistic.This paper proves the consistency of chi-squared test with varying number of classes under some conditions.Meanwhile,the authors also give a convergence rate of KolmogorovSimirnov distance between the test statistic and corresponding chi-square distributed random variable.In addition,a real example and simulation results validate the reasonability of theoretical result and the superiority of chi-squared test with varying number of classes.
