Stochastic Leibnitz Rule for Markovian HJM models

[damperwer]

Hi all,

I am reading the differential form of the short rate equation for markov HJM model. In that the following is used..
(d \int_0^t f(s,t) d W_s = f(t,t) d W_t + \large( \int_0^t \frac{\partial f(s,t)}{\partial t} d W_s \right) dt)

I can't derive this. Can someone please help me?

 

[koupparis]

Total derivative Leibniz rule. Should be straightforward. See http://en.wikipedia.org/wiki/Leibniz_integral_rule