Let{ξt,t∈Zd}be a nonuniform 4-mixing strictly stationary real random field with Efo=0,E|f0²+6<∞for some 0<8<1.A sufficient condition is given for the sequence of partial sum set-indexed process{Zn(A),...Let{ξt,t∈Zd}be a nonuniform 4-mixing strictly stationary real random field with Efo=0,E|f0²+6<∞for some 0<8<1.A sufficient condition is given for the sequence of partial sum set-indexed process{Zn(A),A E A}to converge to Brownian motion.By a direct calculation,the author ahows that the result holds for a more general class of set index A,where A is assurned only to have the metric entropy exponentr,0<r<1.and the rate of nonuniform p-mixing is weakened.The result obtained essentially improve those given by Chen[1)and Goldie,Greenwood[6],etc.展开更多
Let {X<sub>n</sub>, n≥1} be a sequence of random variables and let S<sub>n</sub>=∑<sub>1≤i≤n</sub>X<sub>i</sub>,<sub>n</sub><sup>-</sup>=σ（...Let {X<sub>n</sub>, n≥1} be a sequence of random variables and let S<sub>n</sub>=∑<sub>1≤i≤n</sub>X<sub>i</sub>,<sub>n</sub><sup>-</sup>=σ（X<sub>i</sub>1≤i≤n）,<sub>n</sub><sup>+</sup>=σ（X<sub>i</sub>,i≥n）,n≥1.展开更多
Let G be a p-mixed Warfield Abelian group and F a field of char F = p ≠ 0. It is proved that if for any group H the group algebras FH and FG are F-isomorphic, then H is isomorphic to G. This presentation enlarges a r...Let G be a p-mixed Warfield Abelian group and F a field of char F = p ≠ 0. It is proved that if for any group H the group algebras FH and FG are F-isomorphic, then H is isomorphic to G. This presentation enlarges a result of W. May argued when G is p-local Warfield Abelian and published in Proc. Amer. Math. Soc. （1988）.展开更多
文摘Let{ξt,t∈Zd}be a nonuniform 4-mixing strictly stationary real random field with Efo=0,E|f0²+6<∞for some 0<8<1.A sufficient condition is given for the sequence of partial sum set-indexed process{Zn(A),A E A}to converge to Brownian motion.By a direct calculation,the author ahows that the result holds for a more general class of set index A,where A is assurned only to have the metric entropy exponentr,0<r<1.and the rate of nonuniform p-mixing is weakened.The result obtained essentially improve those given by Chen[1)and Goldie,Greenwood[6],etc.
文摘Let {X<sub>n</sub>, n≥1} be a sequence of random variables and let S<sub>n</sub>=∑<sub>1≤i≤n</sub>X<sub>i</sub>,<sub>n</sub><sup>-</sup>=σ（X<sub>i</sub>1≤i≤n）,<sub>n</sub><sup>+</sup>=σ（X<sub>i</sub>,i≥n）,n≥1.
文摘Let G be a p-mixed Warfield Abelian group and F a field of char F = p ≠ 0. It is proved that if for any group H the group algebras FH and FG are F-isomorphic, then H is isomorphic to G. This presentation enlarges a result of W. May argued when G is p-local Warfield Abelian and published in Proc. Amer. Math. Soc. （1988）.
