Distribution dependent reflecting stochastic differential equations

To characterize the Neumann problem for nonlinear Fokker-Planck equations,we investigate distribution dependent reflecting stochastic differential equations(DDRSDEs)in a domain.We first prove the well-posedness and establish functional inequalities for reflecting stochastic differential equations with singular drifts,and then extend these results to DDRSDEs with singular or monotone coefficients,for which a general criterion deducing the well-posedness of DDRSDEs from that of reflecting stochastic differential equations is established.

Distribution dependent stochastic differential equations

Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications,distribution dependent stochastic differential equations(DDSDEs)have been intensively investigated.In this paper,we summarize some recent progresses in the study of DDSDEs,which include the correspondence of weak solutions and nonlinear Fokker-Planck equations,the well-posedness,regularity estimates,exponential ergodicity,long time large deviations,and comparison theorems.

A Multi-Level Selective Maintenance Strategy Combined to Data Mining Approach for Multi-Component System Subject to Propagated Failures

In several industrial fields like air transport,energy industry and military domain,maintenance actions are carried out during downtimes in order to maintain the reliability and availability of production system.In such a circumstance,selective maintenance strategy is considered the reliable solution for selecting the faulty components to achieve the next mission without stopping.In this paper,a novel multi-level decision making approach based on data mining techniques is investigated to determine an optimal selective maintenance scheduling.At the first-level,the age acceleration factor and its impact on the component nominal age are used to establish the local failures.This first decision making employed K-means clustering algorithm that exploited the historical maintenance actions.Based on the first-level intervention plan,the remaining-levels identify the stochastic dependence among components by relying upon Apriori association rules algorithm,which allows to discover of the failure occurrence order.In addition,at each decision making level,an optimization model combined to a set of exclusion rules are called to supply the optimal selective maintenance plan within a reasonable time,minimizing the total maintenance cost under a required reliability threshold.To illustrate the robustness of the proposed strategy,numerical examples and a FMS real study case have been solved.