The Density of the Distribution of the Maximum of a Gaussian Process

1976 ◽  
Vol 20 (4) ◽  
pp. 847-856 ◽  
Author(s):  
V. S. Tsirel’son
Keyword(s):  
Gaussian Process ◽  
Distribution Of The Maximum

An asymptotic formula for the distribution of the maximum of a Gaussian process with stationary increments

1985 ◽  
Vol 22 (02) ◽  
pp. 454-460 ◽  
Author(s):  
Simeon M. Berman
Keyword(s):  
Asymptotic Formula ◽  
Gaussian Process ◽  
Variance Function ◽  
Stationary Increments ◽  
Distribution Of The Maximum

Let X(t), t≧0, be a Gaussian process with mean 0 and stationary increments. If the incremental variance function σ 2(t) is convex and σ 2(t) = o(t) for t → 0, then P(max[o,t] X(s) > u) ~ P(X(t) > u) for u → ∞ and each t > 0.

A gaussian process with parabolic covariances

1991 ◽  
Vol 28 (04) ◽  
pp. 898-902 ◽  
Author(s):  
Enrique M. Cabaña
Keyword(s):  
Gaussian Process ◽  
Brownian Bridge ◽  
Stationary Gaussian Process ◽  
String Equation ◽  
Distribution Of The Maximum ◽  
Close Relationship ◽  
Vibrating String

The centred, periodic, stationary Gaussian process X(z), ≧ z ≧ 1 with covariances , appears when one studies the solutions of the vibrating string equation forced by noise, corresponding to the case of a finite string with the extremes tied together. The close relationship between this process and a Brownian bridge permits us to compute the distribution of the maximum excursion of the string at particular times.

An asymptotic formula for the distribution of the maximum of a Gaussian process with stationary increments

1985 ◽  
Vol 22 (2) ◽  
pp. 454-460 ◽  
Author(s):  
Simeon M. Berman
Keyword(s):  
Asymptotic Formula ◽  
Gaussian Process ◽  
Variance Function ◽  
Stationary Increments ◽  
Distribution Of The Maximum

Let X(t), t≧0, be a Gaussian process with mean 0 and stationary increments. If the incremental variance function σ2(t) is convex and σ2(t) = o(t) for t → 0, then P(max[o,t]X(s) > u) ~ P(X(t) > u) for u → ∞ and each t > 0.

A gaussian process with parabolic covariances

1991 ◽  
Vol 28 (4) ◽  
pp. 898-902 ◽  
Author(s):  
Enrique M. Cabaña
Keyword(s):  
Gaussian Process ◽  
Brownian Bridge ◽  
Stationary Gaussian Process ◽  
String Equation ◽  
Distribution Of The Maximum ◽  
Close Relationship ◽  
Vibrating String

The centred, periodic, stationary Gaussian process X(z), ≧ z ≧ 1 with covariances , appears when one studies the solutions of the vibrating string equation forced by noise, corresponding to the case of a finite string with the extremes tied together. The close relationship between this process and a Brownian bridge permits us to compute the distribution of the maximum excursion of the string at particular times.

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