Amart-like Sequences
Z Wang · Huadong Shifan Daxue xuebao. Ziran kexue ban · 1985
Let (Ω,??, P) be a probability space, (??_n) an increasing sequence of σ-algebras contained in ??.Let T be the set of all bounded stopping time.An integrable adapted sequence (x_n,??_n) is an amart if X(τ,σ)→0(L~1), where X(τ,σ)=E(x_τ,??_σ)-x_σ,τ,σ∈T.An integrable adapted sequence (x_n,??_n) is an amart-like sequence if X(s,t)→0(L~1) or [X(s,t)]~ ±→0(L~1), where s(t)∈T or ∈N={1, 2,……}.Here, these amart like sequences are proved to have nine classes, and the connections between these classes are discussed.