A simplified proof of the representation of functionals of diffusions (Q1823544)

The result that a functional of the path of a Markov diffusion is the stochastic integral of an integrand which is the conditional expectation of a Fréchet derivative is obtained by first considering the case when the functional depends only on the trajectory value at a fixed time and using flows, similarly to the paper of the reviewer and \textit{M. Kohlmann}, Stat. Probab. Lett. 6, No.5, 327-329 (1988; Zbl 0645.60053). The case of a general functional is then derived by approximation.