We propose sieve M-estimator for a semi-functional linear model in which the scalar response is explained by a linear operator of functional predictor and smooth functions of some real-valued random variables.Spline e...We propose sieve M-estimator for a semi-functional linear model in which the scalar response is explained by a linear operator of functional predictor and smooth functions of some real-valued random variables.Spline estimators of the functional coefficient and the smooth functions are considered,and by selecting appropriate knot numbers the optimal convergence rate and the asymptotic normality can be obtained under some mild conditions.Some simulation results and a real data example are presented to illustrate the performance of our estimation method.展开更多
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 purpose of this paper is to prove that the quadratic variations of smooth It process in the sense of Malliavin-Nualart can be approximated in Sobolev spaces over the Wiener space by its discrete quadratic variations.
基金Supported by the Science and the Technology Program for Guangdong Province(2012B010100044)the Science and Technological Program for Dongguan Higher Education,and the Science and Research Institutions(2012108102031)
基金supported by National Natural Science Foundation of China(Grant Nos.71420107025,11071022,11231010 and 11471223)the Innovation Foundation of Beijing University of Aeronautics and Astronautics for Ph.D.graduates(Grant No.YWF-14-YJSY-027)+2 种基金the National High Technology Research and Development Program of China(863 Program)(Grant No.SS2014AA012303)Beijing Center for Mathematics and Information Interdisciplinary Sciences,Key Project of Beijing Municipal Educational Commission(Grant No.KZ201410028030)Youth Doctor Development Funding Project for"121"Human Resources of Central University of Finance and Economics(Grant No.QBJ1423)
文摘We propose sieve M-estimator for a semi-functional linear model in which the scalar response is explained by a linear operator of functional predictor and smooth functions of some real-valued random variables.Spline estimators of the functional coefficient and the smooth functions are considered,and by selecting appropriate knot numbers the optimal convergence rate and the asymptotic normality can be obtained under some mild conditions.Some simulation results and a real data example are presented to illustrate the performance of our estimation method.
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.
文摘The purpose of this paper is to prove that the quadratic variations of smooth It process in the sense of Malliavin-Nualart can be approximated in Sobolev spaces over the Wiener space by its discrete quadratic variations.
