Abstract
In this paper, we present a direct perturbative method to solving certain Fokker–Planck equations, which have constant diffusion coefficients and some small parameters in the drift coefficients. The method makes use of the connection between the Fokker–Planck and Schrödinger equations. Two examples are used to illustrate the method. In the first example, the drift coefficient depends only on time but not on space. In the second example, we consider the Uhlenbeck–Ornstein process with a small drift coefficient. These examples show that such perturbative approach can be a useful tool to obtain approximate solutions of Fokker–Planck equations with constant diffusion coefficients.
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