Abstract
This paper provides a sufficient condition (on the vector field $\bff(x)$), under which the stationary Fokker–Planck equation $\Delta u-{\rm div}\,(u{\bf f})=0$ has a solution in the form of probability density. The stochastic differential equation with the drift ${\bf f}(x)$ has an invariant probabilistic measure under this condition. This condition is satisfied by some vector fields ${\bf f}$ (drifts) having a sequence of fixed locally stable points, which tends to infinity. Sometimes the proposed method turns out to be more effective than previously known methods based on the Lyapunov function.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have