The following PDE arises in a problem of finding the stationary measure of a 2d system of stochastic differential equations (see this math.stackexchange post): $ $ \mathcal{A}p=0, \quad p\in C^2(\mathbb{R}\times[0,1]) \tag1$ $ where $ $ \mathcal{A}=-x\partial_y[y(1-y)\cdot]+\frac12 x^2\partial^2_y[y^2(1-y)^2\cdot]+x\partial_x+\frac12\partial^2_x+q(x)\partial_x. \tag2 $ $ Here, $ q(x)=\partial_x\log p_1(x)$ , where $ p_1(x)\propto e^{-x^2}$ . The role of $ p_1(x)$Read more