Efficient Simulation for the Maximum of Infinite Horizon Gaussian Processes (with C. Li).

Summary:

This paper is the first to develop an asymptotically optimal algorithm for the maximum of Gaussian process with negative drift (possibly non-linear) and with arbitrary correlation structure (not even stationary is needed for the increments). A feature that I really like is that only elementary calculus is used for the whole construction. The paper also includes a non-standard description for the conditional distribution of Brownian motion with drift -1 given it hits a positive level in finite time. Obviously such conditional process is Brownian motion with drift 1. The nice thing is that the description given in the paper is not even Markovian. It is based on a bridge-sampling scheme in which the anchor point is placed randomly according to a specific distribution and the middle of the process is imputed given the anchor point. The advantage of this description is that it can be directly to any Gaussian process and in fact it is shown to be asymptotically optimal.

Bibtex:

@Article{BlanLi2009,

author = {J. Blanchet and C. Li},

title = {Efficient simulation for the maximum of infinite horizon discrete-time Gaussian processes},

journal = {Journal of Applied Probability},

year = {Forthcoming},

volume = {},

pages = {}

}