A toolbox on the distribution of the maximum of Gaussian process

In this paper we are interested in the distribution of the maximum, or the maximum of the absolute value, of certain Gaussian processes for which the result is exactly known.

[1]  D. Andrews Tests for Parameter Instability and Structural Change with Unknown Change Point , 1993 .

[2]  S. Berman Excursions above high levels for stationary Gaussian processes. , 1971 .

[3]  J. Azaïs,et al.  Level Sets and Extrema of Random Processes and Fields , 2009 .

[4]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[5]  D. Slepian The one-sided barrier problem for Gaussian noise , 1962 .

[6]  David M. De Long Crossing probabilities for a square root boundary by a bessel process , 1981 .

[7]  A. Borodin,et al.  Handbook of Brownian Motion - Facts and Formulae , 1996 .

[8]  Kai Lai Chung,et al.  A Course in Probability Theory , 1949 .

[9]  Benzion Boukai An explicit expression for the distribution of the supremum of brownian motion with a change point , 1990 .

[10]  A. Estrella CRITICAL VALUES AND P VALUES OF BESSEL PROCESS DISTRIBUTIONS: COMPUTATION AND APPLICATION TO STRUCTURAL BREAK TESTS , 2003, Econometric Theory.

[11]  M. Abramowitz,et al.  Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55) , 1965 .

[12]  G. F. Newell,et al.  Zero Crossing Probabilities for Gaussian Stationary Processes , 1962 .

[13]  Projections on spherical cones, maximum of Gaussian fields and Rice's method , 2003 .

[14]  Luisa Beghin,et al.  On the maximum of the generalized Brownian bridge , 1999 .

[15]  A. Rodrigues,et al.  One-Sided Test for an Unknown Breakpoint: Theory, Computation, and Application to Monetary Theory , 2005 .

[16]  W. Feller,et al.  An Introduction to Probability Theory and Its Applications, Vol. II , 1972, The Mathematical Gazette.