In this paper, by means of auxiliary functions and inequalities, we obtain some sufficient conditions of second order nonhomogeneous delay differential equation belonging to the L.S. or L.S. ∩ L.C..
By virtue of an auxiliary function with parameters m, n∈R ,we obtain some new results for quadratic integrability and boundedness of all solutions of second order nonlinear differential equation The theorems obtained...By virtue of an auxiliary function with parameters m, n∈R ,we obtain some new results for quadratic integrability and boundedness of all solutions of second order nonlinear differential equation The theorems obtained in this paper improve and generalize some existing results.展开更多
We study deviation inequalities for some quadratic Wiener functionals and moderate deviations for parameter estimators in a linear stochastic differential equation model.Firstly,we give some estimates for Laplace inte...We study deviation inequalities for some quadratic Wiener functionals and moderate deviations for parameter estimators in a linear stochastic differential equation model.Firstly,we give some estimates for Laplace integrals of the quadratic Wiener functionals by calculating the eigenvalues of the associated HilbertSchmidt operators.Then applying the estimates,we establish deviation inequalities for the quadratic functionals and moderate deviation principles for the parameter estimators.展开更多
基金This research was supported by the NECC of China (03074)Shandong Province (Y2001A03).
文摘In this paper, by means of auxiliary functions and inequalities, we obtain some sufficient conditions of second order nonhomogeneous delay differential equation belonging to the L.S. or L.S. ∩ L.C..
基金Project supported by NNSF of China (19771053) NSF of Shandong (Q97A05116).
文摘By virtue of an auxiliary function with parameters m, n∈R ,we obtain some new results for quadratic integrability and boundedness of all solutions of second order nonlinear differential equation The theorems obtained in this paper improve and generalize some existing results.
基金National Natural Science Foundation of China(Grant Nos. 11171262,11571262 and 11101210)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20130141110076)+1 种基金the Fundamental Research Funds for the Central Universities(Grant No.NS2015074)China Postdoctoral Science Foundation(Grant Nos.2013M531341 and 2016T90450)
文摘We study deviation inequalities for some quadratic Wiener functionals and moderate deviations for parameter estimators in a linear stochastic differential equation model.Firstly,we give some estimates for Laplace integrals of the quadratic Wiener functionals by calculating the eigenvalues of the associated HilbertSchmidt operators.Then applying the estimates,we establish deviation inequalities for the quadratic functionals and moderate deviation principles for the parameter estimators.
