Jonathan Goodman
Courant Institute
New York University
We discuss ways to measure errors in time-stepping methods for solving stochastic differential equations. We argue that "strong error", the expected difference between the computed and actual trajectory, has the undesirable feature that it refers to more than statistical properties of computed paths. "Weak error", statistical error at a particular time, does not capture more detailed properties of random paths such as first hitting times. A proposed compromise is "microscopic total variation measure", which is the error in the joint distribution of the path observed at all the time steps. We present a simple Runge Kutta method whose error is to that of Milstein's method, from this point of view.
This is joint work with Peter Glynn