Isotropic random fields on systems of spheres. (English. Russian original) Zbl 0835.60046

Kuznetsova, O. M.

Theory Probab. Math. Stat. 47, 71-76 (1993); translation from Teor. Jmovirn. Mat. Stat. 47, 69-75 (1992).

Summary: An orthogonal decomposition of an isotropic random field on the Cartesian product \({\mathfrak F} = M \times S_\infty\), where \(M\) is an arbitrary set and \(S_\infty\) is the unit sphere in a separable Hilbert space \(H\), is described. In the case of homogeneous and isotropic random fields, as well as of random fields with homogeneous and isotropic increments on \(H\) or on a finite-dimensional Lobachevskij space \(L_\infty\), a spectral representation of the components of the decomposition is presented.

MSC:

60G60

Random fields

Keywords:

orthogonal decomposition of an isotropic random field; random fields with homogeneous and isotropic increments; spectral representation