Accelerating diffusions
Accelerating diffusions
Let U be a given function defined on ℝd and π(x) be a density function proportional to exp−U(x). The following diffusion X(t) is often used to sample from π(x), $$dX(t)=-\nabla U(X(t))\,dt+\sqrt{2}\,dW(t),\qquad X(0)=x_{0}.$$ To accelerate the convergence, a family of diffusions with π(x) as their common equilibrium is considered, $$dX(t)=\bigl(-\nabla U(X(t))+C(X(t))\bigr)\,dt+\sqrt{2}\,dW(t),\qquad …