Asymptotic characterisation of nonlinear stochastic differential equations with state--independent noise: continuous dynamics, rapid decay and numerical schemes

报告人： Prof John Appleby, Dublin City University

报告题目：Asymptotic characterisation of nonlinear stochastic differential equations with state--independent noise: continuous dynamics, rapid decay and numerical schemes

报告摘要：In this talk, we consider a globally stable ordinary differential equation which is perturbed by a state--independent noise term. We give necessary and sufficient conditions on the asymptotic behaviour of the diffusion coefficient under which solutions of the resulting SDE are a.s. asymptotically convergent to the equilibrium of the original unperturbed equation. We then show how a semi--implicit method can recover this asymptotic behaviour under discretisation. Finally, we consider continuous time SDEs where the nonlinearity may have an infinite derivative at the equilibrium. In this case, we again characterise the rates of convergence of the solution, and show how the semi--implicit method, now modified to have a deterministic but time--varying step size, can recover the precise asymptotic behaviour. These methods of interest, because corresponding (tamed) explicit methods, which are successful in capturing stability may nevertheless unable to recover the rates of decay of solutions.

报告时间：2018年7月9日（周一） 上午 10：30

报告地点：徐汇校区3号楼332（报告厅）

欢迎各位老师和同学们！