Probability of error deviations for the dependent sampling Monte Carlo methods: Exponential bounds in the uniform norm
- Kurbanmuradov, Orazgeldy
- Sabelfeld, Karl
2010 Mathematics Subject Classification
- 65C05 60F10 65C50
2008 Physics and Astronomy Classification Scheme
- Moderately large deviations, dependent sampling Monte Carlo, exponential bound for probability of error deviation, optimal asymptotics
Under Bernstein's condition a non-asymptotic exponential estimation for the probability of deviations of a sum of independent random fields in uniform norm is proposed. Application of this result to the problem of the error estimation for the dependent sampling Monte Carlo method is presented. It is shown that in the domain of moderately large deviations the suggested estimations have optimal asymptotics.