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An innovative theoretical framework for stochastic dynamics based on adecomposition of a stochastic differential equation (SDE) has been developedwith an evident advantage in connecting deterministic and stochastic dynamics,as well as useful applications in physics, engineering, chemistry and biology.It introduces the A-type stochastic integration for SDE beyond traditionalIto's or Stratonovich's interpretation. Serious question on its uniqueness wasrecently raised. We provide here both mathematical and physical demonstrationsthat the uniqueness is guaranteed. Such discussion leads to a betterunderstanding on the robustness of the novel framework. We also discuss thelimitation of a related approach of obtaining potential function from steadystate distribution.

On Uniqueness of "SDE Decomposition" in A-type Stochastic Integration