Let $f:[0,T]\times\Theta\to\mathbb R$ and let $\{B_t\}_{t\in [0,T]}$be a Brownian motion.
Consider the Wiener integral
$$\int_0^T f(t,\theta)dB_t.$$
I am looking for conditions that ensure that $$\frac{d}{d\theta}\int_0^T f(t,\theta)dB_t=\int_0^T \partial_{\theta}f(t,\theta)dB_t$$
In this and this article conditions are set in the case in which $f$ is not deterministic.
Thanks in advance.