Cross-Border Internet of Things E-Commerce Warehouse Control System Based on TRIZ Theory

Cross-border e-commerce of the Internet of Things is affected by international situations and political factors. Supply chain interruption and returns will cause violent fluctuations in commodity inventory, making the inventory control of cross-border e-commerce very difficult. The TRIZ principle is utilized to solve the problem of the difficulty to evaluate the suppliers comprehensively in e-commerce warehouse management. The Markov algorithm is used to describe the change of inventory level. The cyclic expected time and cost function are constructed by the horizontal crossing method, updating the process and Martingale theory. The effect of the correlation between the demand and supply interruption on the optimal inventory control strategy is studied by simulation. The change of the optimal control strategy under the different interrupt and return types is analyzed, and the validity of the management system is verified.

Martingales

This chapter summarizes the essentials of sequential conditioning and martingale theory. After a review with examples of the basic properties of martingales and semi‐martingales, including the Doob decomposition, the upcrossing inequality and martingale convergence are studied and also the role of the conditional variances in establishing convergence. The important martingale inequalities of Kolmogorov, Doob, Burkholder, and Azuma are proved.

A Reliability Growth Process Model with Time-Varying Covariates and Its Application

The nonhomogeneous Poisson process model with power law intensity, also known as the Army Materiel Systems Analysis Activity (AMSAA) model, is commonly used to model the reliability growth process of many repairable systems. In practice, it is necessary to test the reliability of the product under different operational environments. In this paper we introduce an AMSAA-based model considering the covariate effects to measure the influence of the time-varying environmental condition. The parameter estimation of the model is typically performed using maximum likelihood on the failure data. The statistical properties of the estimation in the model are comprehensively derived by the martingale theory. Further inferences including confidence interval estimation and hypothesis tests are designed for the model. The performance and properties of the method are verified in a simulation study, compared with the classical AMSAA model. A case study is used to illustrate the practical use of the model. The proposed approach can be adapted for a wide class of nonhomogeneous Poisson process based models.

Stochastic Theory of Coarse-Grained Deterministic Systems: Martingales and Markov Approximations

Many works have been devoted to show that Thermodynamics and Statistical Physics can be rigorously deduced from an exact underlying classical Hamiltonian dynamics, and to resolve the related paradoxes. In particular, the concept of equilibrium state and the derivation of Master Equations should result from purely Hamiltonian considerations. In this chapter, we reexamine this problem, following the point of view developed by Kolmogorov more than 60 years ago, in great part known from the work published by Arnold and Avez in 1967. Our setting is a discrete time dynamical system, namely the successive iterations of a measure-preserving mapping on a measure space, generalizing Hamiltonian dynamics in phase space. Using the notion of Kolmogorov entropy and martingale theory, we prove that a coarse-grained description both in space and in time leads to an approximate Master Equation satisfied by the probability distribution of partial histories of the coarse-grained state.

Moderate Laws of Large Numbers via Weak Laws

By a $moderate$ $law$ $of$ $large$ $numbers$ we mean any theorem whose conclusion includes the $L^{p}$-vanishment of the sequence of the sample means of some centered random variables with $1 \leq p < +\infty$ given.Given any $1 \leq p < +\infty$ and any $\eps > 0$,we prove a moderate law of large numbers for $L^{p+\eps}$-bounded random variables that obey a weak law.Thus our moderate laws in particular complement those obtained from the martingale theory,and establish the counterintuitive fact that (for$L^{p+\eps}$-bounded random variables) where there is a weak law there is a moderate law.

Multiobjective Lightning Flash Algorithm Design and Its Convergence Analysis via Martingale Theory

In this paper, a novel multiobjective lightning flash algorithm (MOLFA) is proposed to solve the multiobjective optimization problem. The charge population state of the lightning flash algorithm is defined, and we prove that the charge population state sequence is a Markov chain. Since the convergence analysis of MOLFA is to investigate whether a Pareto optimal solution can be reached when the optimal charge population state is obtained, the development of a charge population state is analyzed to achieve the goal of this paper. Based on the martingale theory, the MOLFA convergence analysis is carried out in terms of the supermartingale convergence theorem, which shows that the MOLFA can reach the global optimum with probability one. Finally, the effectiveness of the proposed MOLFA is verified by a numerical simulation example.