Generalized Feynman integrals via conditional Feynman integrals
The paper is a continuing exercise by the authors to arrive at the most generalized version of Feynman integrals studied by Cameron and his collaborators. The starting point is the Wiener integral \(\int_{C_ 0[0,T)} F(\lambda^{-1/2} Z(x,.)+\xi) (\lambda^{-1/2} Z(x,T)+\xi)m(dx)\) where \(Z\) is the Gaussian process \(Z(x,t)=\int^ t_ 0 h(s)dx(s)\) with \(h\) in \(L_ 2[0,T]\) and the integral on the right-hand side denotes the Paley-Wiener-Zygmund stochastic integral. The authors make free use of their earlier results relating to the theory of conditional Feynman integral and obtain formulae for the analytic operator-valued Feynman integrals of various classes of functionals.
Paley-Wiener-Zygmund stochastic integral
scientific article; zbMATH DE number 474976