how to interprete that the random forces in Langevin Equation are assumed to be delta-correlated I mean that, is there anything more fundamental to yields the result that the random force in Langevin Equation is delta-correlated?
As is shown in the picture of a textbook below, its formula (3.4) is given by the assumption that "impacts are independent".However, it is still daunted for me to derive delta-correlated function from it.
Maybe there are fundamental concepts or derivation steps I should work on, which I will be appreciated of if you could point out generously.

 A: Delta-correlation is just an approximation. The actual forces that they represent are not truly delta-correlated. However, typical atomic-scale force autocorrelations last ~ 1 picosecond, so it's a pretty good approximation.
EDIT. To clarify, imagine dividing time up into tiny slices (~ 1 ps). The stochastic force experienced by the particle at time $t_i$ will be random with a mean of zero (i.e. Eq. 3.3). At the next time slice, $t_{i+1}$, a different stochastic force will be acting also with a mean zero. If the collisions that cause these two forces are independent then their product must have zero mean. This follows from the fact that when two random variables $X$ and $Y$ are independent of each other, the expectation of their product is the product of their means,
$$ \langle XY\rangle=\langle X\rangle\langle Y\rangle $$
or, in this instance,
$$ \langle F_a(t_i)F_a(t_{j\neq i}) \rangle = \langle F_a(t_i)\rangle\langle F_a(t_{j\neq i})\rangle=0 $$
See the Expectation of product of random variables.
