On pathwise super-exponential decay rates of solutions of scalar nonlinear stochastic differential equations

摘要

This paper studies the pathwise asymptotic stability of the zero solution of scalar stochastic differential equation of Ito type. In particular, we provide conditions for solutions to converge to zero at a given rate, which is faster than any exponential rate of decay, The results completely classify the rates of decay of many parameterised families of stochastic differential equations.