Exponential Inequalities in Calibration Problems with Gaussians Errors

Abstract

This article establishes exponential inequalities for the probability of the distance between the approximated solution and the exact one for a calibration problem. We consider an operator equation taking the following form Ax = u, where A is a compact operator. We assume that the right-hand side u is not known exactly, and we have only its approximation by using the process of gaussian error.

Keywords:

• Calibration
• Cramer condition
• Linear operator

Mathematics Subject Classification:

• 65N21
• 53C38