Incremental delta-sigma ADC
An incremental sigma delta coder operates from a reset, rather than continuously. That is why it is examined in transient operation, because that's how it works.

The Signal Transfer function and the Noise Transfer function are still applicable to the modulator. The filter is no longer a simple linear filter which would also yield to those analyses, but a non-linear optimal filter, that knows the form of the modulator.

In practice the gains attributable to incremental operation are somewhat application dependent. For low order low resolution, the technique certainly allows reduced power consumption. However it runs into problems with higher orders of modulator, as it needs to know the matching between the stages accurately. This is the whole point of using sigma delta with a linear filter, the modulator component matching does not need to be precise.