A satellite network system comprises three layers of satellites:LEO(Low Earth Orbit),MEO(Middle Earth Orbit)and GEO(Geostationary Orbit).In the system,users can choose a layer according to their demands,including QoS(...A satellite network system comprises three layers of satellites:LEO(Low Earth Orbit),MEO(Middle Earth Orbit)and GEO(Geostationary Orbit).In the system,users can choose a layer according to their demands,including QoS(Quality of Service),congestion,energy cost,etc.The utility that users gain will change when they access satellites in different layers.The mobility of satellites in the LEO and MEO leads to frequent handover among satellites in the same layer.These characteristics of multi-layered satellite networks make it possible for us to exploit the optimal distribution of users,which will maximize the utility of the entire satellite network.While the proposed problem is an NP-hard problem,we analyze the system based on the Markov chain and use the Markov approximation to approach the maximum utility.In addition,we use the count down and select algorithm to implement the process of Markov chain.The simulation results validate the convergence of the Markov approximation.In addition,the gap between the approximate value and optimal values decreases with an increase inβ,which is a positive constant in Markov formulation,according to the simulation results.展开更多
The momentum wheel assumes a dominant role as an inertial actuator for satellite attitude control systems.Due to the effects of structural aging and external interference,the momentum wheel may experience the gradual ...The momentum wheel assumes a dominant role as an inertial actuator for satellite attitude control systems.Due to the effects of structural aging and external interference,the momentum wheel may experience the gradual emergence of irreversible faults.These fault features will become apparent in the telemetry signal transmitted by the momentum wheel.This paper introduces ADTWformer,a lightweight model for long-term prediction of time series,to analyze the time evolution trend and multi-dimensional data coupling mechanism of satellite momentum wheel faults.Moreover,the incorporation of the approximate Markov blanket with the maximum information coefficient presents a novel methodology for performing correlation analysis,providing significant perspectives from a data-centric standpoint.Ultimately,the creation of an adaptive alarm mechanism allows for the successful attainment of the momentum wheel fault warning by detecting the changes in the health status curves.The analysis methodology outlined in this article has exhibited positive results in identifying instances of satellite momentum wheel failure in two scenarios,thereby showcasing considerable promise for large-scale applications.展开更多
This work is concerned with rates of convergence of numerical methods using Markov chainapproximation for controlled diffusions with stopping (the first exit time from a bounded region).In lieuof considering the assoc...This work is concerned with rates of convergence of numerical methods using Markov chainapproximation for controlled diffusions with stopping (the first exit time from a bounded region).In lieuof considering the associated finite difference schemes for Hamilton-Jacobi-Bellman (HJB) equations,a purely probabilistic approach is used.There is an added difficulty due to the boundary condition,which requires the continuity of the first exit time with respect to the discrete parameter.To prove theconvergence of the algorithm by Markov chain approximation method,a tangency problem might arise.A common approach uses certain conditions to avoid the tangency problem.Here,by modifying thevalue function,it is demonstrated that the tangency problem will not arise in the sense of convergencein probability and in L^1.In addition,controlled diffusions with a discount factor is also treated.展开更多
The state equations of stochastic control problems,which are controlled stochastic differential equations,are proposed to be discretized by the weak midpoint rule and predictor-corrector methods for the Markov chain a...The state equations of stochastic control problems,which are controlled stochastic differential equations,are proposed to be discretized by the weak midpoint rule and predictor-corrector methods for the Markov chain approximation approach. Local consistency of the methods are proved.Numerical tests on a simplified Merton's portfolio model show better simulation to feedback control rules by these two methods, as compared with the weak Euler-Maruyama discretisation used by Krawczyk.This suggests a new approach of improving accuracy of approximating Markov chains for stochastic control problems.展开更多
Risks embedded in asset price dynamics are taken to be accumulations of surprise jumps.A Markov pure jump model is formulated on making variance gamma parameters deterministic functions of the price level.Estimation i...Risks embedded in asset price dynamics are taken to be accumulations of surprise jumps.A Markov pure jump model is formulated on making variance gamma parameters deterministic functions of the price level.Estimation is done by matrix exponentiation of the transition rate matrix for a continuous time finite state Markov chain approximation.The motion is decomposed into a space dependent drift and a space dependent martingale component.Though there is some local mean reversion in the drift,space dependence of the martingale component renders the dynamics to be of the momentum type.Local risk is measured using market calibrated measure distortions that introduce risk charges into the lower and upper prices of two price economies.These risks are compensated by the exponential variation of space dependent arrival rates.Estimations are conducted for the S&P 500 index(SPX),the exchange traded fund for the financial sector(XLF),J.P.Morgan stock prices(JPM),the ratio of JPM to XLF,and the ratio of XLF to SPX.展开更多
基金supported by the National Natural Science Foundation of China(Nos.61325012,61428205,91438115,61532012,61671478,61672342).
文摘A satellite network system comprises three layers of satellites:LEO(Low Earth Orbit),MEO(Middle Earth Orbit)and GEO(Geostationary Orbit).In the system,users can choose a layer according to their demands,including QoS(Quality of Service),congestion,energy cost,etc.The utility that users gain will change when they access satellites in different layers.The mobility of satellites in the LEO and MEO leads to frequent handover among satellites in the same layer.These characteristics of multi-layered satellite networks make it possible for us to exploit the optimal distribution of users,which will maximize the utility of the entire satellite network.While the proposed problem is an NP-hard problem,we analyze the system based on the Markov chain and use the Markov approximation to approach the maximum utility.In addition,we use the count down and select algorithm to implement the process of Markov chain.The simulation results validate the convergence of the Markov approximation.In addition,the gap between the approximate value and optimal values decreases with an increase inβ,which is a positive constant in Markov formulation,according to the simulation results.
基金supported by the Science Center Program of National Natural Science Foundation of China(62188101)the National Natural Science Foundation of China(61833009,61690212,51875119)+1 种基金the Heilongjiang Touyan Teamthe Guangdong Major Project of Basic and Applied Basic Research(2019B030302001)
文摘The momentum wheel assumes a dominant role as an inertial actuator for satellite attitude control systems.Due to the effects of structural aging and external interference,the momentum wheel may experience the gradual emergence of irreversible faults.These fault features will become apparent in the telemetry signal transmitted by the momentum wheel.This paper introduces ADTWformer,a lightweight model for long-term prediction of time series,to analyze the time evolution trend and multi-dimensional data coupling mechanism of satellite momentum wheel faults.Moreover,the incorporation of the approximate Markov blanket with the maximum information coefficient presents a novel methodology for performing correlation analysis,providing significant perspectives from a data-centric standpoint.Ultimately,the creation of an adaptive alarm mechanism allows for the successful attainment of the momentum wheel fault warning by detecting the changes in the health status curves.The analysis methodology outlined in this article has exhibited positive results in identifying instances of satellite momentum wheel failure in two scenarios,thereby showcasing considerable promise for large-scale applications.
基金supported in part by the National Science Foundation under Grant Nos. DMS-0624849 and DMS-0907753in part by the Natural Science Foundation of China under Grant No. #70871055
文摘This work is concerned with rates of convergence of numerical methods using Markov chainapproximation for controlled diffusions with stopping (the first exit time from a bounded region).In lieuof considering the associated finite difference schemes for Hamilton-Jacobi-Bellman (HJB) equations,a purely probabilistic approach is used.There is an added difficulty due to the boundary condition,which requires the continuity of the first exit time with respect to the discrete parameter.To prove theconvergence of the algorithm by Markov chain approximation method,a tangency problem might arise.A common approach uses certain conditions to avoid the tangency problem.Here,by modifying thevalue function,it is demonstrated that the tangency problem will not arise in the sense of convergencein probability and in L^1.In addition,controlled diffusions with a discount factor is also treated.
基金supported by the China Postdoctoral Science Foundation (No.20080430402).
文摘The state equations of stochastic control problems,which are controlled stochastic differential equations,are proposed to be discretized by the weak midpoint rule and predictor-corrector methods for the Markov chain approximation approach. Local consistency of the methods are proved.Numerical tests on a simplified Merton's portfolio model show better simulation to feedback control rules by these two methods, as compared with the weak Euler-Maruyama discretisation used by Krawczyk.This suggests a new approach of improving accuracy of approximating Markov chains for stochastic control problems.
文摘Risks embedded in asset price dynamics are taken to be accumulations of surprise jumps.A Markov pure jump model is formulated on making variance gamma parameters deterministic functions of the price level.Estimation is done by matrix exponentiation of the transition rate matrix for a continuous time finite state Markov chain approximation.The motion is decomposed into a space dependent drift and a space dependent martingale component.Though there is some local mean reversion in the drift,space dependence of the martingale component renders the dynamics to be of the momentum type.Local risk is measured using market calibrated measure distortions that introduce risk charges into the lower and upper prices of two price economies.These risks are compensated by the exponential variation of space dependent arrival rates.Estimations are conducted for the S&P 500 index(SPX),the exchange traded fund for the financial sector(XLF),J.P.Morgan stock prices(JPM),the ratio of JPM to XLF,and the ratio of XLF to SPX.
