Abstract
Metropolized integrators for ergodic stochastic differential equations (SDEs) are proposed that (1) are ergodic with respect to the (known) equilibrium distribution of the SDEs and (2) approximate pathwise the solutions of the SDEs on finitetime intervals. Both these properties are demonstrated in the paper, and precise strong error estimates are obtained. It is also shown that the Metropolized integrator retains these properties even in situations where the drift in the SDE is nonglobally Lipschitz, and vanilla explicit integrators for SDEs typically become unstable and fail to be ergodic.
Original language | English (US) |
---|---|
Pages (from-to) | 655-696 |
Number of pages | 42 |
Journal | Communications on Pure and Applied Mathematics |
Volume | 63 |
Issue number | 5 |
DOIs | |
State | Published - May 2010 |
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics