\begin{align} & F_n(\theta)=\int_0^T f_{n}(t,\theta(t)) \, dt \\[6pt] & f_n(t,\xi)=\int_\Omega\mathcal{L}(X(t) + Z_n(t,\omega),Y(t),\xi (\omega)) + R_n(\xi(\omega)) Pd(\omega) \end{align}
where $ t\in [0,T]$, $ \xi \in L^2(\Omega,R^d)$ For every fixed $n,$ I want to prove that $F$ has a minimum. Any arbitrary assumptions can be made about the integrand.
