Polynomial Recurrence for SDEs with a Gradient-Type Drift, Revisited

In this paper, polynomial recurrence bounds for a class of stochastic differential equations with rotational symmetric gradient type drift and an additive Wiener process are established, as well certain priori moment inequalities solutions. The key feature paper is that the approach does not use Lyapunov functions because it clear how to construct them. method based on Dynkin’s (nonrandom) chain applied instead. Another asymptotic conditions potential near infinity assumed inequalities—which allows more flexibility compared single limit at infinity, making less restrictive.