This paper investigates Itô-type stochastic linear quadratic controller design for uncertain model of vehicle suspension. The Itô stochastic model of quarter-car is constructed considering parametric stochastic perturbations in stiffness and damping characteristics of suspension. To tackle with uncertainties of model, a stochastic optimal control law is obtained applying stochastic Hamilton-Jacobi-Bellman equation. By means of Itô lemma and stochastic extension of Lyapunov method, stochastic stability of the closed-loop system is guaranteed. The stochastic optimal controller is designed for a general form of Itô uncertain model which is comprised multi-dimensional multiplicative perturbations and then it is implemented on perturbed model of vehicle suspension. Furthermore, it is shown that the separation principal does not hold for the system with state multiplicative noise; therefore, the synthesized observer-based controller guarantees the stability of augmented dynamic consists of system and estimation error dynamics. A simulation study is performed to evaluate the effectiveness of stochastic optimal control approach in satisfying objectives of active suspension. To this end, time and frequency responses of ride comfort and road holding characteristics are demonstrated for two specific road cases including sinusoidal bump and ISO random profile.

Chi-Kwang Li, Bit-Shun Tam and Nam-Kiu Tsing have obtained necessary and sufficient condition for a linear operator on linear space of generalized doubly stochastic matrices to be strong preserver of doubly stochastic matrices and permutation matrices. We show if a linear operator T : Mm → Mn is a (strong) preserver of doubly stochastic matrices, then T is a (strong) preserver of the linear manifold of r-generalized doubly stochastic matrices and the linear space of generalized doubly stochastic matrices. Also we give necessary and sufficient condition for a linear operator T : Mm → Mn to be (strong) preserver of doubly stochastic matrices and permutation matrices.

In this we article study the common rules of stochastic dominance (first order stochastic dominance, second and third) also the concept of stochastic dominance are discussed in the context of real behaviour of investors. thus has been studied the Investor’s behavior toward growth-value stocks based on rules of stochastic dominance in listed companies at TSE. The results don’t showed first, second and third order of stochastic dominance of Growth stocks over value stocks and value stocks over Growth stocks.

The aim of this manuscript is to introduce and analyze a stochastic finite difference scheme for Ito stochastic partial differential equations. We also discuss the consistency, stability, and convergence for the stochastic finite difference scheme. The numerical simulations obtained from the proposed stochastic finite difference scheme show the efficiency of the suggested stochastic finite difference scheme.

The source of randomness in stochastic systems is an input with stochastic behavior as treated in the existing literature. Special types of stochastic processes such as the Wiener process or the Brownian motion have served as an adequate model of such an input for years. The body of stochastic systems theory is elegantly shaped around such input models. An example is the Itô’s formula. With development of new applications, we are faced with various phenomena that are more demanding from a stochastic modeling approach.To cope with this problem we restate the stochastic Lyapunov theorem such that it can be applied to a wider class of stochastic systems. In this paper stochastic systems are considered without imposing assumptions on the nature of the stochastic input and the way it affects the sample trajectories. Lyapunov stability theorem is represented for this type of systems in terms of a stability notion that generalizes the notion of stability in moments. As a result, the new theorem finds a larger domain of applications while it can be reduced to some known versions of the stochastic Lyapunov theorem.As an application, an existing deterministic result for nonlinear networked control systems is extended to a more practical probabilistic setting which extends the available analysis tools for checking the stability of continuous-time nonlinear networked control systems in the stochastic setting. The results are applied to a two-channel magnetic levitation system which is controlled over a local communication network to obtain a bound on the rate of transmission failures due to the presence of noise in the industrial environment.

Due to the importance of using an accurate stochastic model in estimation of the coordinates of points using the GNSS observation method, this study investigates the role of the elevation angle-dependent stochastic model. The least-squares estimation method is usually used in processing GNSS observations. This method requires the use of two essential models, one is functional model and the other is stochastic model. The functional model illustrates the relationship between observations and unknown parameters. The stochastic model presents the covariance matrix and the statistical properties (expectation) and dispersion of errors in observation, which expresses the accuracy and the correlation between the types of observations. A precise and detailed stochastic model for observations, expresses the receiver's internal noise, residual errors, and the correlation between the variables. Moreover, by choosing a suitable stochastic model, we can provide the necessary preconditions for solving the reliable phase ambiguity and precise positioning. In this study, we investigate and compare 9 stochastic models based on the satellite elevation angle. These 9 models are expressed as equations of four families of trigonometric functions , , improved trigonometric functions, and exponential functions. To do this, we use observations of a single point in two time epoch where simulated displacement was applied to it very precisely by the device. First, by using precise point positioning method, the horizontal coordinates of the point in two epochs were estimated by using 9 stochastic models. According to the accomplished comparison, we present the closest estimated value to the simulated real value of the stochastic models which are trigonometric functions , improved trigonometric functions and exponential functions respectively. Among these four models, The results of exponential function is closest to the simulated real value. Online services are then used to process point-of-view observations, according to which the two OPUS and AUSPOS services are most closest to the simulated real observations. Then the estimation of the accuracy of the horizontal components is examined by means of 9 presented stochastic models. According to the presented results, the highest accuracy and least error are related to the use of stochastic model  (improved trigonometric functions). Then, two stochastic models and matrix weights  and  (exponential functions) showed the highest accuracy. Using these three models with the highest accuracy, the average accuracy obtained for the East component is between 0.03 mm and 2.8 mm and for the North component is between 0.04 mm and 3.1 mm. In the next section, due to the accuracy obtained for the horizontal coordinate components in all epochs (sampling interval of 5 s) using these three stochastic models, fewer epochs are required to reach the level of accuracy of Dosimeter, Centimeter and Millimeter. In such a way that, for desired point, 277 epochs for the East component and 405 epochs for the North component are required to reach the millimeter precision level. Finally, considering the 5cm convergence condition for the horizontal components East and North, due to the three models used, this convergence condition is achievable after 5 minutes and 50 seconds for the East component and after 8 minutes and 5 seconds for the component North.

Nowadays, advances in numerical methods have led to model real-life physical problems effectively. One of the difficulties in modelling the real-life physical problems is the geometric creation, because the mesh definition for a complex geometry is hard. In order to overcome this issue, one can use the spectral cell method due to employing a Cartesian mesh even for a complex geometry, such that constant Jacobian is considered for cells in the mesh. Spectral cell method is a combination of the spectral element method and the fictious domain concept, which uses an adaptive integration employing the quadtree or octree partitioning for the cells intersecting arbitrary boundaries as well as the cells including nonuniform material distribution. The interpolation functions of Lobatto family of spectral elements are utilized in spectral cell method. The spectral cell method is an efficient numerical method to solve the governing equations of continuum structures with complicated geometries. On the other hand, uncertainty naturally exists in the parameters of an engineering system (e.g., elastic modulus) and the input of that system (e.g., loading). Thus, the effects of those uncertainties are important in the response calculation of the engineering system. There are two types of uncertainty: aleatoric and epistemic. Aleatoric uncertainty is defined as an intrinsic variability of certain quantities, while epistemic uncertainty is defined as a lack of knowledge about certain quantities. An alternative to a deterministic modelling is a stochastic modelling, but analysing such a stochastic model is harder than a deterministic model having deterministic material properties and configuration. This is because the behaviour of the stochastic model is inevitably stochastic. Traditionally, Monte-Carlo simulation analyses a stochastic model by generating numerous realizations of the stochastic problem, and then solves each one like a deterministic problem. Nevertheless, Monte-Carlo simulation needs very high computational cost, particularly for large-scale problems. A systematic technique for uncertainty quantification is the stochastic finite element method providing a variety of statistical information. However, the method is computationally expensive with respect to the finite element method, and thus there are many developments for stochastic methods. Consequently, this paper presents stochastic form of spectral cell method to solve elastostatic problems considering material uncertainties. Therefore, uncertainty quantification of an elastostatic problem with geometrically complex domain can be modelled more efficiently than the traditional stochastic finite element method. In the proposed method, Fredholm integral equation is discretised using spectral cell method to solve Karhunen-Loève expansion used for the random field decomposition. Also, this method uses fewer cells than the stochastic finite cell method, and does not require formation of the eigenfunctions. In addition, Karhunen-Loève and polynomial chaos expansions are used to decompose the random field and to consider the response variability, respectively. Simple mesh generation, desirable accuracy and computational cost are the main features of the present method. In this study, two benchmark numerical examples are provided to demonstrate the efficiency and capabilities of the proposed method in the solution of elastostatic problems. The results are compared to those of stochastic finite element method and stochastic spectral element method.

Some properties of the geometric stochastic process (GSP) are studied along with those of a related process which we propose to call the Double geometric stochastic process (DGSP), under certain conditions. This process also has the same advantages of tractability as the geometric stochastic process; it exhibits some properties which may make it a useful complement to the multiple Trends geometric stochastic process. Also, it may be fit to observed data as easily as the geometric stochastic process. As a first attempt, the proposed model was applied to model the data and the Coronavirus epidemic in Iraq to reach the best model that represents the data under study. A chicken swarm optimization algorithm is proposed to choose the best model representing the data, in addition to estimating the parameters a, b, (mu), and (sigma^{2}) of the double geometric stochastic process, where (mu) and (sigma^{2}) are the mean and variance of (X_{1}), respectively.

The stochastic neuron has great importance in neural networks and is one of the most important subjects in machine learning algorithms. Hardware implementation of neural networks has always been of interest to researchers and can significantly increase the performance and applications of neural networks. Hence hardware implementation of the stochastic neuron is also important. In this paper, utilizing stochastic behavior of MTJs in subcritical current regime a hardware model for stochastic neurons is proposed. Using HSpice tool, the proposed model was simulated and simulation results show that the proposed model functionality is similar to the mathematical description of the stochastic neuron and the error of this model is always less than 4.8% compared to the mathematical description of the stochastic neuron. Also using corner simulation, it was shown that this model performs properly even in the presence of process variation and its error rate is less than 15.46% and 17.43% compared to the mathematical model and ideal simulation, respectively.

The stochastic computing (SC) method is a low-cost alternative to conventional binary computing that processes digital data in the form of pseudo-random bit-streams in which bit-flip errors have a trivial effect on the signal final value because of the highly redundant encoding format of this method. As a result, this computational method is used for fault-tolerant digital applications. In this paper, stochastic computing has been chosen to implement 2-dimensional discrete wavelet transform (2-D DWT) as a case study. The performance of the circuit is analyzed through two different faulty experiments. The results show that stochastic 2-D DWT outperforms binary implementation. Although SC provides inherent fault tolerance, we have proposed four structures based on dual modular redundancy to improve SC reliability. Improving the reliability of the stochastic circuits with the least area overhead is considered the main objective in these structures. The proposed methods are applied to improve the reliability of stochastic wavelet transform circuits. Experimental results show that all proposed structures improve the reliability of stochastic circuits, especially in extremely noisy conditions where fault tolerance of SC is reduced.