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The COVID-19 epidemic is still spreading globally and will not be completely over in a short time. Wearing a mask is an effective means to combat the spread of COVID-19. However, whether the public wear a mask for epidemic prevention and control will be affected by stochastic factors such as vaccination, cultural differences and irrational emotions, which bring a high degree of uncertainty to the prevention and control of the epidemic. The purpose of this study is to explore and analyze the epidemic prevention and control strategies of the public in an uncertain environment.

Based on the stochastic evolutionary game model of the Moran process, the study discusses the epidemic prevention and control strategies of the public under the conditions of the dominance of stochastic factors, expected benefits and super-expected benefits.

The research shows that the strategic evolution of the public mainly depends on stochastic factors, cost-benefit and the number of the public. When the stochastic factors are dominant, the greater the perceived benefit, the lower the cost and the greater the penalty for not wearing masks, the public will choose to wear a mask. Under the dominance of expected benefits and super-expected benefits, when the number of the public is greater than a certain threshold, the mask-wearing strategy will become an evolutionary stable strategy. From the evolutionary process, the government’s punishment measures will slow down the speed of the public choosing the strategy of not wearing masks. The speed of the public evolving to the stable strategy under the dominance of super-expected benefits is faster than that under the dominance of expected benefits.

The study considers the impact of stochastic factors on public prevention and control strategies and provides decision-making support and theoretical guidance for the scientific prevention of the normalized public.

To the best of the authors’ knowledge, no research has considered the impact of different stochastic interference intensities on public prevention and control strategies. Therefore, this paper can be seen as a valuable resource in this field.

Most of the previous work on reliability analysis was based on the traditional reliability theory. The calculated results can only reflect the reliability of components at a specific time, which neglects the uncertainty of load and resistance over time. The purpose of this paper is to develop a time-dependent reliability analysis approach based on stochastic process to deal with the problem and apply it to the structural design of railway vehicle components.

First, the parametric model of motor hanger for electric multiple unit (EMU) is established by ANSYS parametric design language, and its structural stress is analyzed according to relevant standards. The Latin hypercube method is used to analyze the sensitivity of the structure, and the uncertainty parameters (sizes and loads) which have great influence on the structural strength are determined. The D-optimal experimental design is carried out to establish the polynomial response surface function, which characterizes the relationship between uncertainty parameters and structural stress. Second, the Poisson stochastic process is adopted to describe the number of loads acting, and the Monte Carlo method is used to obtain the load acting history according to its probability distribution characteristics. The load history is introduced into the response surface function and the uncertainty of other parameters is considered at the same time, and the stress history of the motor hanger is obtained. Finally, the degradation process of structural resistance is described by a Gamma stochastic process, and the time-dependent reliability of the motor hanger is calculated based on the reliability theory.

Time and the uncertainties of parameters have great impact on reliability. The results of reliability decrease with time fluctuation are more reasonable, stable and credible than traditional methods.

In this paper, the proposed method is applied to the structural design of the motor hanger for EMU, which has a good guiding significance for accurately evaluating whether if the design meets the reliability requirements.

The value of this paper is that the method takes both the randomness of load over time and the uncertainty of structural parameters in the design and manufactures process into consideration, and describes the monotonous degradation characteristics of structural resistance. At the same time, the time-dependent reliability of mechanical components is calculated by a response surface method. It not only improves the accuracy of reliability analysis, but also improves the analysis efficiency and solves the problem that the traditional reliability analysis method can only reflect the static reliability of components.

This paper aims to present two-stage network models in the presence of stochastic ratio data.

Black-box, free-link and fix-link techniques are used to apply the internal relations of the two-stage network. A deterministic linear programming model is derived from a stochastic two-stage network data envelopment analysis (DEA) model by assuming that some basic stochastic elements are related to the inputs, outputs and intermediate products. The linkages between the overall process and the two subprocesses are proposed. The authors obtain the relation between the efficiency scores obtained from the stochastic two stage network DEA-ratio considering three different strategies involving black box, free-link and fix-link. The authors applied their proposed approach to 11 airlines in Iran.

In most of the scenarios, when alpha in particular takes any value between 0.1 and 0.4, three models from Charnes, Cooper, and Rhodes (1978), free-link and fix-link generate similar efficiency scores for the decision-making units (DMUs), While a relatively higher degree of variations in efficiency scores among the DMUs is generated when the alpha takes the value of 0.5. Comparing the results when the alpha takes the value of 0.1–0.4, the DMUs have the same ranking in terms of their efficiency scores.

The authors innovatively propose a deterministic linear programming model, and to the best of the authors’ knowledge, for the first time, the internal relationships of a two-stage network are analyzed by different techniques. The comparison of the results would be able to provide insights from both the policy perspective as well as the methodological perspective.

The depth and breadth of the market for contingent claims, including exotic options, has expanded dramatically. Regulators have expressed concern regarding the risks of exotics to the financial system, due to the difficulty of hedging these instruments. Recent literature focuses on the difficulties in hedging exotic options, e.g., liquidity risk and other violations of the standard Black‐Scholes model. This article provides insight into hedging problems associated with exotic options: 1) hedging in discrete versus continuous time, 2) transaction costs, 3) stochastic volatility, and 4) non‐constant correlation. The author applies simulation analysis of these problems to a variety of exotics, including Asian options, barrier options, look‐back options, and quanto options.

Discusses the efficiency of a cybernetic approach to non‐oscillatory luminescence processes, generated by perturbed biosystems, and applies it to oscillatory luminescence processes. Constructs multiplicative stochastic models of oscillatory bio‐ and chemiluminescence processes, generated by some perturbed/stimulated biosystems (a temperature‐stimulated soybean root system, light‐stimulated microporocytes of larch, antiviral drug‐treated vero cells infected by Herpes simplex virus). Determines a correlation structure for these models by analysing their transfer functions. Uses the memory function approach to compare and contrast the oscillatory processes with their non‐oscillatory analogs. Formulates a hypothesis about the dependence between the persistence and the oscillatory behaviour of biosystems and proposes stochastic perturbation measures founded on those multiplicative models.

The purpose of this paper is to review the life of the famous mathematician Kiyosi Itô and discuss his influence on the study of agricultural finance and agricultural economics.

This paper is a qualitative historical review.

The paper provides a biographical stretch of Itô's life. It is shown that his influence started to infiltrate the agricultural economics profession at around 1985 and is currently a major influence of a range of economic issues from farm policy to agricultural investments.

The biography is limited to a review of Itô's academic life and influence.

The paper offers a historical perspective on how probability emerged as a critical piece of the economic puzzle. For scholars and practitioners of agricultural finance, the paper provides an in depth review of how Itô processes have, and can, be used.

This paper provides a historical perspective on Itô that is of use to students and scholars of rural credit. This is the first “biography” of Itô to discuss his influence on agricultural finance and agricultural economics.

The purpose of this paper is to investigate how to determine optimal investing stopping time in a stochastic environment, such as with stochastic returns, stochastic interest rate and stochastic expected growth rate.

Transformation method was used for solving optimal stopping problem by providing a way to transform path‐dependent problem into a path‐independent one. Based on option pricing theory, optimal investing stopping time was thought of as an optimal executed timing problem of American‐style option.

First, the authors transform a path‐dependent stop timing problem to a path‐independent one with transformation under very general conditions, to directly use the existing conclusion of optimal stopping time literature. Second, when dynamics of capital growth is homogeneous, the authors changed the two dimensional optimal stop timing problem into a single dimension problem based on the assumption of zero exercise costs. Third, the authors investigated the comparative dynamics about asset selling boundary on asset value, state variable and return predictability. With constant discount rate and growth rate, the optimal selling timing depends on the simple comparison between capital cost and growth rate.

The paper's contributions to analysis method may be as follows. The authors demonstrate how to transform a path‐dependent stopping problem into a path‐independent one under general conditions. The transform method in this article can be applied to other path‐dependent optimal stopping problems. In particular, a Riccati ordinary differential equation for the transformation is set up. In most examples commonly met in finance, the equation can be solved explicitly.

The purpose of this paper is to define the related concepts and theorems about the second moment process in stochastic analysis on time scales.

The study on stochastic analysis now includes two special conditions, namely discrete and continual conditions. However, in some cases, conditions are time scales, so that a new concept, namely stochastic analysis on time scales, is needed. Applying the time scales theory to the second moment process in stochastic analysis, related concept foundation of stochastic analysis on time scales has been established.

The need for the theory about stochastic analysis on time scales is recognized.

This is a very useful theory in related fields in future.

Stochastic analysis on time scales expand applying fields of stochastic analysis, and will be helpful to related fields.

Introduction Operations research, i.e. the application of scientific methodology to operational problems in the search for improved understanding and control, can be said to have started with the application of mathematical tools to military problems of supply bombing and strategy, during the Second World War. Post‐war these tools were applied to business problems, particularly production scheduling, inventory control and physical distribution because of the acute shortages of goods and the numerical aspects of these problems.

A new approach to living organisms with irreversibly perturbed homeostatis, based on the integrated moving average IMA (0,1,1) and autoregressive‐integrated moving average ARIMA (1,2,1) linear stochastic models of non‐stationary photon emission processes, is proposed. The approach consists of introducing a stochastic formulation of the transfer function and memory functional into a general description of non‐equilibrium states of perturbed organisms. A memory function‐based quantitative measure of perturbed biohomeostasis has also been proposed and discussed.