result of this paper, we establish a commuting diagram of unraveling and low-rank approximation, with the proposed [SDLR]{} method.

The rest of the paper is organized as follows. In [Section \[sec::sdlr\]]{}, we shall formulate the [stochastic dynamical [low-rank]{} approximation]{} method in the space of finite signed measures. Then in [Section \[sec::example\]]{}, we will provide a concrete example, in which a low-rank dynamics for [Fokker-Planck]{} equation is derived, as well as the low-rank dynamics of the SDE for that [Fokker-Planck]{} equation. The comparison of our method and DO method will also be given at the end of [Section \[sec::example\]]{}. [[ Consistency of our low-rank approximation and error analysis will be provided in [Section \[sec::error\]]{}. In [Section \[sec::discuss::unravel\]]{}, we shall establish the connection between the action of dynamical low-rank approximation and the action of unraveling. We will prove a commuting relation between them.]{}]{} Then numerical results will be presented in [Section \[sec::numerics\]]{} to demonstrate the performance. In [Section \[sec::conclusion\]]{}, we will give a brief summary and some potential follow-up work.

Throughout this paper, ${\left\lVert\cdot\right\rVert}_{{HS}}$ means Hilbert-Schmidt norm (or Frobenius norm as in linear algebra). Bold letters, like ${{\boldsymbol{U}}}$ and ${{\boldsymbol{G}}}$ [*etc*.]{}, represent matrices (linear operators). Also, ${\left[\cdot, \cdot\right]_{-}}$ is commutator and ${\left[\cdot, 