In this particular example (below), the use of the word "instantaneous" is relevant, while "dispersion" here has a rather different meaning, ie the frequency dependence of propagation speed. In your case, "dispersion" refers to the statistical dispersion, ie variability, of whatever is being measured.
http://rose.bris.ac.uk/dspace/bitstream/1983/354/1/fitton_IE...
Note that the meanings of "instant" and "instantaneous" are rather different. For example, my instantaneous speed as measured by a roadside camera might be 40mph (having slowed down for it), while my mean speed over a 2 mile stretch might be 50mph. If my speed is quite constant, then the dispersion in the mph values will be low. On the other hand, if my clutch is dodgy, then the dispersion (ie the standard deviation) in mph values will be high, even though the mean speed may be the same. In terms of how "instantaneous" a measure of instantaneous dispersion (or mean) can be, this discussion could get quite technical...
The translation workplace 
