Browse Teach Curate

Projected Milstein Method for Order-One Approximation of Random Periodic Solutions of SDEs

An explicit projected Milstein scheme (PMM) that approximates random periodic solutions of semi-linear SDEs with multiplicative noise and non-globally Lipschitz coefficients over an infinite time horizon. The random periodic solution is recovered as the limit of the pull-back of the discretized SDE, and a moment-bound-free error analysis proves strong (mean-square) convergence of order one, improving the order-half rate of prior explicit schemes for multiplicative noise.

Rosie Text

Order-one explicit approximations of random periodic solutions of semi-linear SDEs with

A random periodic solution is a stochastic analogue of a periodic orbit that captures the long-time, periodically-forced behaviour of a stochastic differential equation (SDE) and generally has no clo…