formula

$&&E\bigg[\prod_{i=0}^kf_i(t_i)g_i(X_{t_i})\bigg]=\\ &&\int_{\mathbf{R}_+\times E}\delta_0\otimes\nu (ds_0\otimes dx_0)f_0(s_0)g_0(X_0)\int_{\mathbf{R}_+\times E}\tilde{P}_{t_1}((s_0,x_0),dt_1\otimes dx_1)f_1(s_1)g_1(X_{t_1})\ldots \\ &&\int_E\tilde{P}_{t_k-t_{k-1}}((s_{k-1}, x_k),ds_k\otimes dx_k)f_k(s_k)g_k(x_k)$