The phrase "analysis of the stochastic" is correct and usable in written English.
It can be used in contexts related to statistics, probability, or any field that involves random processes or variables.
Example: "The analysis of the stochastic processes revealed significant patterns in the data that were previously overlooked."
Alternatives: "examination of the stochastic" or "study of the stochastic".
Based on the analysis of the stochastic properties of the received signals, several detectors are studied and evaluated.
For the analysis of the stochastic characteristics of a homogenized elastic property, the first-order perturbation method is used.
Limiting the investigation to voltage clamped conditions facilitated a more thorough mathematical analysis of the stochastic shielding approximation, but also restricted the biological applicability of the results.
The analysis of the stochastic model of the process led to the condition for the asymptotic stochastic stability, which determines the region of asymptotic stability with probability one.
Munteanu et al. [8] have presented a review of both the operational methods for the analysis of the stochastic data and the reconstruction of the detailed stochastic evolution equations from the available data.
Owing to the complexity of geo-engineering seepage problems influenced by different random factors, three-dimensional simulation and analysis of the stochastic seepage field plays an important role in engineering applications.
The mutual arrangement of these intervals and Allee threshold are used in the geometrical analysis of the various stochastic regimes in this model: stable stochastic oscillations around nontrivial equilibrium, noise-induced extinction, and stochastic trigger.
HMMs relate the two quantities in a framework which eliminates the necessity of direct sample-wise correlations, and avoid direct time-series analysis complications of the stochastic wind speed data at a marginal expense of easy pressure measurements.
The main novelty introduced by the authors is taking into account intrinsic stochasticity of the (de phosporylation processes and analytical analysis of the resulting stochastic mathematical model (which is in remarkable agreement with the simulation results).
The proof is based on a careful analysis of the associated stochastic flow of characteristics.
Based on the analysis of the robust stochastic finite-time stability and the H ∞ performance, the filter design method is obtained.
