## MAGP (Example results)

Let *X* be a Gaussian process with mean and
covariance functions denoted by:

We assume regularity conditions imposed in Mercadier (2006).

Let *M(a,b)* denotes the maximum of *X* over the interval *[a,b]*:

MAGP computes (by lower and upper bounds) the distribution of
the maximum *M(a,b)* when *X* is centered.

The estimation of
*P[M(a,b)>u]* is given by the command
**magp(r,a,b,u,option)**. Consequently, this toolbox allows for
instance:

- the
approximation of the pdf of
*M(a,b)*; - the analysis of
the behaviour of
*{M(0,T)>u}*when*T*varies (see below); - ...

Example 1 -- Stationary case with:

syms x y r=exp(-(x-y)^2/2); % Bounds for P( M(0,1)> 1 ): magp(r,0,1,1,500) ans = 0.2533 0.2541 % Plot the bounds of the function T -> P( M(0,T) > 1 ) obtained by MAGP: