On the variation of the difference of singular components in the skorokhod problem and on stochastic differential systems in a half-space

Abstract

In this work we derive a representation for the variation of the difference of singular components in the Skorokhod problem. in which besides the other terms the integrals from some local times are presented. In the special cases when these local times turn out to be identically equal to zero, we come to the bound of the above-mentioned variation which, in turn, is applied to the investigation of the existence and uniqueness of a strong solution of the stochastic differential system in a half-space and to the estimation of the distance in variation between the local times of two reflected (at zero) stochastic processes with the same diffusion and different drift coefficients

Keywords:

• Skorokhod problem
• singular components
• distance in variation
• local times
• reflexion in a half-space
• strong solution