stochastic model

Recently, the optimization issue relevance of reinforced concrete (RC) structures design solutions through the maximum use of their bearing capacity resource has increased significantly; in turn, solving this issue depends on a fundamental understanding of the reliability and durability concepts. Because any loads, impacts, or bearing capacity reserve parameters are random variables, there is a need to build stochastic models, which can become the “reliability design” concept base shortly.

An application of path integral method to Merton and Vasicek stochastic models of interest rate is considered.  Two approaches to a path integral construction are shown.  The first approach consists in using Wieners measure with the following substitution of solutions of stochastic equations into the models.  The second approach is realised by using transformation from Wieners measure to the integral measure related to the stochastic variables of Merton and Vasicek equations.  The introduction of boundary conditions is considered in the second approach in order to remove incorrect time asym

Questions of the mathematics modeling of local and global processes of Geodynamics are examined. The model of the process must take into account all its sources at the same time. This demand can be ensured by simultaneously calculating variations from all results of observations of geodynamic features. This task is solved by the determination and use of properties of covariance functions for fields of observation results.