Sentence examples for use the stochastic analysis from inspiring English sources

Based on a hierarchical multiscale approach on the mesoscopic level, in this study we use the stochastic analysis and the computational homogenization method to analyse the effect of thickness and stiffness of the interphase region on the overall elastic properties of the clay/epoxy nanocomposites.

Firstly we have constructed the control function by using the stochastic analysis technique, it is very important for us to study the approximate controllability.

By using the stochastic analysis techniques and novel integral inequalities, some sufficient conditions for the solvability of the addressed problem are derived.

A new set of sufficient conditions is obtained to achieve the required result by using the stochastic analysis theory and fixed point strategy.

By using the stochastic analysis techniques, sufficient conditions are first derived such that the filtering error system is guaranteed to have the desired security level, and then the filter gain is parameterized by using the semi-definite programme method with certain nonlinear constraints.

By using the stochastic analysis theory and differential inequality technology, we firstly obtain sufficient conditions for persistence in the mean and extinction.

In the stochastic case, by using the stochastic analysis technique and the methods directly from deterministic control problems, Sakthivel et al. [12] considered the approximate controllability of fractional stochastic evolution equations.

Subsequently, by using the stochastic analysis techniques, the properties of operator semigroup and combining those new integral inequalities, we will attempt to give the global attracting sets of the considered system.

Open image in new window Fig. 13 Sequence of design variables used for the stochastic analysis.

Further, the finite element model was used to perform the stochastic analysis using Monte Carlo simulation.

The proposed method is developed in this paper to improve the conventional MPCA-based method by extending the time-domain analysis into the time frequency using the stochastic model analysis.