Mean anisotropy of homogeneous Gaussian random fields and anisotropic norms of linear translation-invariant operators on multidimensional integer latticeстатья
Информация о цитировании статьи получена из
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 27 января 2016 г.
Аннотация:Sensitivity of output of a linear operator to its input can be quantified in various ways.
In Control Theory, the input is usually interpreted as disturbance and the output is to
be minimized in some sense. In stochastic worst-case design settings, the disturbance
is considered random with imprecisely known probability distribution. The prior set of
probability measures can be chosen so as to quantify how far the disturbance deviates
from the white-noise hypothesis of Linear Quadratic Gaussian control. Such deviation
can be measured by the minimal Kullback-Leibler informational divergence from the
Gaussian distributions with zero mean and scalar covariance matrices. The resulting
anisotropy functional is defined for finite power random vectors. Originally, anisotropy
was introduced for directionally generic random vectors as the relative entropy of the
normalized vector with respect to the uniform distribution on the unit sphere. The
associated a-anisotropic norm of a matrix is then its maximum root mean square or
average energy gain with respect to finite power or directionally generic inputs whose
anisotropy is bounded above by a>=0. We give a systematic comparison of the anisotropy
functionals and the associated norms. These are considered for unboundedly growing
fragments of homogeneous Gaussian random fields on multidimensional integer lattice
to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are
extended to bounded linear translation invariant operators over such fields.