random process discretization; random field discretization; quantization; lattice quantization; sampling; sampling design; estimation of stochastic process, estimation of stochastic field; estimation of integral of stochastic process; estimation of integral of random field.

Subject:

My scientific interests are in the field of discretization of stochastic process and fields. There were only few works in the Russia on this theme, that is why the main results were achieved in other countries. The main idea of it is that the stochastic problems of discretization of random pocesses and fields can be realize as non-stochastic problems (mainly as the quantization problems). So all of the quantization theory results can be aplied to these problems, and many achievements of the stochastic process and fields discretization theory can be realize as the quantization theory one. There are many results on the discretization of stochastic process, of uniform isotropic (stationary) random fields, of non-uniform (but locally isotropic) random fields. I have posed a problem of the optimal discretization of non-isotropic random field in the form that allows to apply all previous achievements in this fields and gives a adequate solution.

A. V. Zakharov, “The macroscopic system of Einstein–Maxwell equations for a system of interacting particles”, TMF, 125:1 (2000), 107–131; Theoret. and Math. Phys., 125:1 (2000), 1391–1412

1983

2.

A. V. Zakharov, “Kinetics of small perturbations in closed and open Friedmann cosmologies”, TMF, 55:2 (1983), 224–235; Theoret. and Math. Phys., 55:2 (1983), 463–470