Two problems of the Monte Carlo method theory

In this paper two nonsolved problems of the Monte Carlo theory are presented. The first of them concernes the uniform boundedness of the "walk on spheres" estimates for the Helmgoltz equation. Another problem is the important example from the minimax Monte Carlo theory for evaluating of many integrals.

mihaylov.pdf1.56 MB

Spectral models of vector-valued random fields

Numerical models of vector-valued random fields are extensively used in solving applied problems. These models have become the subject of many investigations. The paper deals with methods of numerical modeling of homogeneous vector-valued random fields based on the spectral decomposition. General relations for spectral models are obtained and particular algorithms...

prigarin.pdf4.41 MB