Generalized conditional Yeh-Wiener integral containing monotonically increasing functions

Abstract

In this paper, we introduce the generalized Yeh-Wiener space and the generalized conditional Yeh-Wiener integral containing the monotonic function. Particularly, we treat the generalized conditional Yeh-Wiener integral containing monotonically increasing functions. To do so, we divide the monotonically increasing and continuous function with finitely many non-differentiable points into two cases and make a suitable partition on the region. Finally, we evaluate the generalized conditional Yeh-Wiener integral for certain functional and show that previous results in [2, 6] can be generalized by results in this paper.