摘要 : Consider events of the form {Z(s) >= zeta (s), s is an element of S}, where Z is a continuous Gaussian process with stationary increments, is a function that belongs to the reproducing kernel Hilbert space R of process Z, and S su... 展开 Consider events of the form {Z(s) >= zeta (s), s is an element of S}, where Z is a continuous Gaussian process with stationary increments, is a function that belongs to the reproducing kernel Hilbert space R of process Z, and S subset of R is compact. The main problem considered in this paper is identifying the function beta* is an element of R satisfying beta*(s) >= zeta (s) on S and having minimal R-norm. The smoothness (mean square differentiability) of Z turns out to have a crucial impact on the structure of the solution. As examples, we obtain the explicit solutions when zeta (s) = s for S is an element of [0, 1] and Z is either a fractional Brownian motion or an integrated Ornstein-Uhlenbeck process. (c) 2006 Elsevier B.V. All rights reserved. 收起