Combining Response Surface Optimization and Stochastic Analysis for Crashworthiness Design – an Introductory Study by Lars A. Fredriksson, Uwe Schramm

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A Stochastic Analysis of the Transient Current Induced along the Thin Wire Scatterer Buried in a Lossy Medium by Silvestar Šesnić, Sébastien Lalléchère, Dragan Poljak, Pierre Bonnet, Khalil El Khamlichi Drissi

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A Probabilistic Assessment Model for Train-Bridge Systems: Special Attention on Track Irregularities by Dejun Liu, Lifeng Xin, Xiaozhen Li, Jiaxin Zhang

“…Numerical studies show that the ergodic properties of track irregularities on spectra, amplitudes, wavelengths, and phases should be taken into account in stochastic analysis of train-bridge interactions. Since the main contributive factors concerning different dynamic indices are rather different, different failure modes possess no obvious or only weak correlations from the probabilistic perspective, and the first-order reliability theory is suitable in achieving the system reliability.…”
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Nonlinear Stochastic SIS Epidemic Model Incorporating Lévy Process by Amine El Koufi

“…We establish sufficient conditions for the extinction and persistence of the disease in the population using some stochastic analysis background. We illustrate our theoretical results by numerical simulations. …”
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Existence and Uniqueness of Mild Solutions for Nonlinear Stochastic Impulsive Differential Equation by L. J. Shen, J. T. Sun

“…By using Schaefer's fixed theorem and stochastic analysis technique, we propose sufficient conditions on existence and uniqueness of solution for stochastic differential equations with impulses. …”
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The Optimal Control and MLE of Parameters of a Stochastic Single-Species System by Huili Xiang, Zhijun Liu

“…With the help of the techniques of stochastic analysis and mathematical statistics, sufficient conditions for the optimal control threshold value, the optimal control moment, and the maximum likelihood estimation of parameters are established, respectively. …”
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Existence and Stability of Almost Periodic Solution for a Stochastic Cellular Neural Network with External Perturbation by Hui Zhou, Zongfu Zhou, Wei Jiang

“…By employing fixed points principle and some stochastic analysis techniques, we establish some sufficient conditions for existence and exponential stability of a quadratic mean almost periodic solution of the model. …”
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Stability Analysis of Stochastic Reaction-Diffusion Cohen-Grossberg Neural Networks with Time-Varying Delays by Chuangxia Huang, Xinsong Yang, Yigang He

“…With the help of Lyapunov method, stochastic analysis, and inequality techniques, a set of new suffcient conditions on pth moment exponential stability for the considered system is presented. …”
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Further Result on Passivity for Discrete-Time Stochastic T-S Fuzzy Systems with Time-Varying Delays by Ting Lei, Qiankun Song, Zhenjiang Zhao

“…By constructing appropriate Lyapunov-Krasovskii functionals and employing stochastic analysis method and matrix inequality technique, a delay-dependent criterion to ensure the passivity for the considered T-S fuzzy systems is established in terms of linear matrix inequalities (LMIs) that can be easily checked by using the standard numerical software. …”
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SOME PECULIAR FEATURES IN SHRINKAGE OF CLAY MASS DURING DRYING PROCESS by I. K. Ivanovsky, S. N. Osipov, L. V. Rafeenkova

“…The paper contains results of correlation and stochastic analysis for regularities in shrinkage of the Lukoml clay and molding mass prepared on its base, and also the Gloukhov and Gloukhovetsky kaolin and their mixtures.It has been revealed that an exponent is the most convenient approximation form of the shrinkage characteristic for the Lukoml clay and molding mass prepared on its base within significant range of moisture changes.After products’ molding in a vacuum press a linear dependence is considered as the most convenient type of approximation within the range of moisture changes and with the main shrinkage.…”
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Dynamical Analysis of a Stochastic Multispecies Turbidostat Model by Yu Mu, Zuxiong Li, Huili Xiang, Hailing Wang

“…First of all, sufficient conditions of the competitive exclusion among microorganisms are obtained by employing the techniques of stochastic analysis. Furthermore, the results demonstrate that the competition among microorganisms and stochastic disturbance will affect the dynamical behaviors of microorganisms. …”
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Stochastic Passivity of Uncertain Neural Networks with Time-Varying Delays by Jianting Zhou, Qiankun Song, Jianxi Yang

“…By constructing appropriate Lyapunov-Krasovskii functionals, and employing Newton-Leibniz formulation, the free-weighting matrix method, and stochastic analysis technique, a delay-dependent criterion for checking the passivity of the addressed neural networks is established in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. …”
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Fractional Stochastic Differential Equations with Hilfer Fractional Derivative: Poisson Jumps and Optimal Control by Fathalla A. Rihan, Chinnathambi Rajivganthi, Palanisamy Muthukumar

“…We study the existence and uniqueness of mild solutions of such a class of fractional stochastic system, using successive approximation theory, stochastic analysis techniques, and fractional calculus. …”
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A Generalization of Itô's Formula and the Stability of Stochastic Volterra Integral Equations by Wenxue Li, Meng Liu, Ke Wang

“…It is well known that Itô’s formula is an essential tool in stochastic analysis. But it cannot be used for general stochastic Volterra integral equations (SVIEs). …”
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Event-Based H∞ Filter Design for Sensor Networks with Missing Measurements by Jinliang Liu, Shumin Fei, Engang Tian

“…By using the Lyapunov stability theory and the stochastic analysis theory, sufficient criteria are derived for the existence of a solution to the algorithm of the event-based filter design. …”
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Novel exact solutions for PDEs with mixed boundary conditions by Mark Craddock, Martino Grasselli, Andrea Mazzoran

“…We are able to obtain nonstandard solutions to equations arising in a range of areas, including mathematical finance, stochastic analysis, hyperbolic geometry, and mathematical physics. …”
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Mean Square Exponential Stability of Stochastic Cohen-Grossberg Neural Networks with Unbounded Distributed Delays by Chuangxia Huang, Lehua Huang, Yigang He

“…With the help of Lyapunov function, stochastic analysis technique, and inequality techniques, some novel sufficient conditions on mean square exponential stability for SCGNN are given. …”
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Analysis of Edge Detection in Bar Code Symbols: An Overview and Open Problems by Saša Krešić-Jurić

“…Starting with the basic statistical properties of speckle patterns, we present stochastic analysis of speckle noise. We derive the autocorrelation function and power spectral density (PSD) of the noise in terms of intensity distribution of the scanning beam. …”
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Finite-Time Nonfragile Dissipative Control for Discrete-Time Neural Networks with Markovian Jumps and Mixed Time-Delays by Ling Hou, Dongyan Chen, Chan He

“…First, by selecting an appropriate Lyapunov-Krasovskii functional and applying stochastic analysis methods, some parameters-dependent sufficient conditions for solvability of stochastic finite-time boundedness are derived. …”
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Exponential Stability of Stochastic Delayed Neural Networks with Inverse Hölder Activation Functions and Markovian Jump Parameters by Yingwei Li, Huaiqin Wu

“…Secondly, by applying the Lyapunov-Krasovskii functional approach, stochastic analysis theory, and linear matrix inequality (LMI) technique, new delay-dependent sufficient criteria are achieved in terms of LMIs to ensure the SNNs with noise perturbations to be globally exponentially stable in the mean square. …”
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