Approximately Optimum Two-Stage Sampling Plans.
We present here the results of the investigation on approximation by the Poisson law of distributions of sums of random variables in the scheme of series. We give the results pertaining to the behaviour of large deviation probabilities and asymptotic expansions, to the method of cumulants, with the aid of which our results have been obtained.
We present a method of numerical approximation for stochastic integrals involving α-stable Lévy motion as an integrator. Constructions of approximate sums are based on the Poissonian series representation of such random measures. The main result gives an estimate of the rate of convergence of finite-dimensional distributions of finite sums approximating such stochastic integrals. Stochastic integrals driven by such measures are of interest in constructions of models for various problems arising...
Consider a system of many components with constant failure rate and general repair rate. When all components are reliable and easily reparable, the reliability of the system can be evaluated from the probability q of failure before restoration. In [14], authors give an asymptotic approximation by monotone sequences. In the same framework, we propose, here, a bounding for q and apply it in the ageing property case.
A stochastic “Fubini” lemma and an approximation theorem for integrals on the plane are used to produce a simulation algorithm for an anisotropic fractional Brownian sheet. The convergence rate is given. These results are valuable for any value of the Hurst parameters Finally, the approximation process is iterative on the quarter plane A sample of such simulations can be used to test estimators of the parameters αi,i = 1,2.