An extension of Stieltjes-Young integrals

Let ƒﾓ(t) and f(t) be real-valued functions defined on a closed interval a, b. The Riemann-Stieltjes integral of f with respect to ƒﾓ is usually denoted by numerical formula When ƒﾓ(x) is of bounded variation on the interval a, b, we can treat this integral in the framework of measure theory. Let p and q are positive numbers such that numerical formula L. C. Young showed that the integral numerical formula in the case that f(t) and ƒﾓ(t) have finite mean variation of order p and q, respectively. In this paper we shall try to extend the Stieltjes-Young integration theory when f(t) and ƒﾓ(t) are stochastic processes.