Band 11, Heft 3

The approximation theorem for an infinite system of interacting stochastic differential equations is proved. This result is applied then for describing the support of the distribution of the solution of this system.

We investigate the asymptotic properties of the maximum likelihood estimator and Bayes estimator of the drift parameter for stochastic processes satisfying linear stochastic differential equations driven by fractional Brownian motion. We obtain a Bernstein-von Mises type theorem also for such a class of processes.

A multivalued ∗ -nonexpansive map is discontinuous. We prove random fixed point theorems for this noncontinuous class of random operators defined on bounded as well as unbounded domains in a Banach space under various boundary conditions. A result regarding random approximation is also derived.

The estimator of the mean-square approximation of 3-D homogeneous and isotropic random field is investigated. The problem of statistical simulation of realizations of random fields in threedimensional space is considered. The algorithm for the receiving of this realization has been formulated, which has been constructed on the base the mean-square approximation of random fields estimator. It has been constructed the statistical model for the Gaussian random fields in three-dimensional space, which has been given by its statistical characteristics.

New facts on absolutely continuity of Gaussian measure under nonlinear transformations containing "random" parameter are established.

Following the recent paper by A. K. Gupta et al . (2002), we generate skew pdfs of the form 2 ƒ ( u ) G (λ u ), where ƒ is taken to be a uniform pdf while the cdf G is taken to come from one of normal, Student's t , Cauchy, Laplace, logistic or uniform distribution. The properties of the resulting distributions are studied. In particular, expressions for the n th moment and the characteristic function are derived. We also provide graphical illustrations and quantify the range of possible values of skewness and kurtosis.