Let { W(t);t≥0 } be a standard Brownian motion.For a positive integer m ,define a Gaussian processX m(t)=1m!∫ t 0(t-s) m d W(s).In this paper the liminf behavior of the increments of this process is discu...Let { W(t);t≥0 } be a standard Brownian motion.For a positive integer m ,define a Gaussian processX m(t)=1m!∫ t 0(t-s) m d W(s).In this paper the liminf behavior of the increments of this process is discussed by establishing some probability inequalities.Some previous results are extended and improved.展开更多
Extending the results of [4] in the univariate case, in this paper we prove that the bivariate interpolation polynomials of Hermite-Fejér based on the Chebyshev nodes of the first kind, those of Lagrange based o...Extending the results of [4] in the univariate case, in this paper we prove that the bivariate interpolation polynomials of Hermite-Fejér based on the Chebyshev nodes of the first kind, those of Lagrange based on the Chebyshev nodes of second kind and ±1, and those of bivariate Shepard operators, have the property of partial preservation of global smoothness, with respect to various bivariate moduli of continuity.展开更多
基金Project Supported by National Science Fundation of China(1 9571 0 2 1 ) and Zhejiang Province
文摘Let { W(t);t≥0 } be a standard Brownian motion.For a positive integer m ,define a Gaussian processX m(t)=1m!∫ t 0(t-s) m d W(s).In this paper the liminf behavior of the increments of this process is discussed by establishing some probability inequalities.Some previous results are extended and improved.
文摘Extending the results of [4] in the univariate case, in this paper we prove that the bivariate interpolation polynomials of Hermite-Fejér based on the Chebyshev nodes of the first kind, those of Lagrange based on the Chebyshev nodes of second kind and ±1, and those of bivariate Shepard operators, have the property of partial preservation of global smoothness, with respect to various bivariate moduli of continuity.
