Journal of the
Korean Mathematical Society JKMS

In this note, we establish a translation theorem in an analogue of Wiener space $(C[0,t],\omega_\varphi )$ and find formulas for the conditional $\omega_\varphi$-integral given by the condition $X(x) = (x(t_0 ), x(t_1 ) , \cdots ,$ $x(t_n ))$ which is the generalization of Chang and Chang's results in 1984. Moreover, we prove a translation theorem for the conditional $\omega_\varphi$-integral.

Keywords: analogue of Wiener measure, translation theorem, conditional $\omega_\varphi$-integral

MSC numbers: 28C20, 28D05, 60A99, 60J65