二阶模糊随机过程均方Henstock-Stieltjes积分的收敛定理

Convergence Theorems of Mean-Square Henstock-Stieltjes Integrals for Second Order Fuzzy Stochastic Process

利用二阶模糊随机过程均方Henstock-Stieltjes积分的定义和性质,讨论了两类二阶模糊随机过程均方Henstock-Stieltjes积分的收敛定理,即二阶模糊随机过程序列关于增实函数收敛定理(ρ)lim n→∞ integral from n=a to b(Xn(t)dg(t))=integral from n=a to b(X(t)dg(t))和均方连续二阶模糊随机过程关于实值单调非减函数列收敛定理(ρ)lim n→∞ integral from n=a to b(X(t)dg(t))=integral from n=a to b(X(t)dg(t)).

In this paper,using definition and properties of mean-square Henstock-Stieltjes integrals for second order fuzzy stochastic process,two convergence theorems of Henstock-Stieltjes are discussed.The two following convergence theorems have been gotten.One is the convergence theorem of a second order fuzzy stochastic process sequence about increasing real function（ρ）lim n→∞ integral from n=a to b（Xn（t）dg（t））= integral from n=a to b（X（t）dg（t））,the other is convergence theorem of mean-square continuous second order fuzzy stochastic process about a non-decreasing real function sequence（ρ）limn→∞ integral from n=a to b（X（t）dg（t））= integral from n=a to b（X（t）dg（t））.These results play important roles in further studying integrability and of differentiability of fuzzy stochastic process.