There are several important generalizations of martingales such as games fairer with time, quasi-mils and sequential martingales in the limit. In the note, we shall consider all possible structures of a probability sp...There are several important generalizations of martingales such as games fairer with time, quasi-mils and sequential martingales in the limit. In the note, we shall consider all possible structures of a probability space （Ω,A, （An）, P） associated with a stochastic basis（An） of sub a-fields of A with An ↑ A. Then, we shall apply them to establish some comparison results for the aforementioned generalizations of martingales.展开更多
A real continuous function which is defined on an interval is said to beA-convex if it is convex on the set of self-adjoint elements,with spectra in the interval,in all matrix algebras of the unital C-algebra A.We giv...A real continuous function which is defined on an interval is said to beA-convex if it is convex on the set of self-adjoint elements,with spectra in the interval,in all matrix algebras of the unital C-algebra A.We give a general formation of Jensen’s inequality for A-convex functions.展开更多
基金Supported by the Natural Science Foundation of the Education Department of Henan province(200510483002)
文摘There are several important generalizations of martingales such as games fairer with time, quasi-mils and sequential martingales in the limit. In the note, we shall consider all possible structures of a probability space （Ω,A, （An）, P） associated with a stochastic basis（An） of sub a-fields of A with An ↑ A. Then, we shall apply them to establish some comparison results for the aforementioned generalizations of martingales.
基金Supported by Shanghai Leading Academic Discipline Project(Grant No.B407)National Natural Science Foundation of China(Grant No.11171109)
文摘A real continuous function which is defined on an interval is said to beA-convex if it is convex on the set of self-adjoint elements,with spectra in the interval,in all matrix algebras of the unital C-algebra A.We give a general formation of Jensen’s inequality for A-convex functions.
