In this paper we study the local measure of approximation of a class of special mathematical expectation operators to Lipschitz class of functions by probabilistic method. The some well known operators (e. g., the Ber...In this paper we study the local measure of approximation of a class of special mathematical expectation operators to Lipschitz class of functions by probabilistic method. The some well known operators (e. g., the Bernstein, Bascakov and Szasz-Mirakjan operators etc) are special cases of a class of the mathematical expetation operators.展开更多
In this article, a sublinear expectation induced by G-expectation is introduced, which is called G- evaluation for convenience. As an application, we prove that for any ξ∈ L β G (Ω T ) with some β > 1 the mart...In this article, a sublinear expectation induced by G-expectation is introduced, which is called G- evaluation for convenience. As an application, we prove that for any ξ∈ L β G (Ω T ) with some β > 1 the martingale decomposition theorem under G-expectaion holds, and that any β > 1 integrable symmetric G-martingale can be represented as an Ito integral w.r.t. G-Brownian motion. As a byproduct, we prove a regularity property for G-martingales: Any G-martingale {M t } has a quasi-continuous version.展开更多
文摘In this paper we study the local measure of approximation of a class of special mathematical expectation operators to Lipschitz class of functions by probabilistic method. The some well known operators (e. g., the Bernstein, Bascakov and Szasz-Mirakjan operators etc) are special cases of a class of the mathematical expetation operators.
基金supported by National Basic Research Program of China (973 Program) (Grant No. 2007CB814902)
文摘In this article, a sublinear expectation induced by G-expectation is introduced, which is called G- evaluation for convenience. As an application, we prove that for any ξ∈ L β G (Ω T ) with some β > 1 the martingale decomposition theorem under G-expectaion holds, and that any β > 1 integrable symmetric G-martingale can be represented as an Ito integral w.r.t. G-Brownian motion. As a byproduct, we prove a regularity property for G-martingales: Any G-martingale {M t } has a quasi-continuous version.