Analogues of conditional Wiener integrals and their change of scale transformations on a function space
- Cho, Dong Hyun
- Kim, Bong Jin
- Yoo, Il
DOIAbstract
AbstractFor a partition 0=t0<t1<⋯<tn<tn+1=t of the interval [0,t], let Xn(x)=(x(t0),…,x(tn)) and Xn+1(x)=(x(t0),…,x(tn),x(tn+1)) on a generalized Wiener space (C[0,t],B(C[0,t]),wφ), where C[0,t] is the space of the continuous paths on [0,t] and wφ is a probability measure on the Borel class B(C[0,t]) of C[0,t]. In this paper, using simple formulas for conditional wφ-integrals on C[0,t] with the conditioning functions Xn and Xn+1, we evaluate the conditional analytic Wiener wφ-integrals of the function Gr having the formGr(x)=F(x)Ψ(∫0tv1(s)dx(s),…,∫0tvr(s)dx(s)), for F∈Swφ which is a Banach algebra, and for Ψ=f+ϕ which need not be bounded or continuous, where f∈Lp(Rr) and ϕ∈Mˆ(Rr). And also, we establish several change of scale transformatio...
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