This work presents an advanced and detailed analysis of the mechanisms of hepatitis B virus(HBV)propagation in an environment characterized by variability and stochas-ticity.Based on some biological features of the vi...This work presents an advanced and detailed analysis of the mechanisms of hepatitis B virus(HBV)propagation in an environment characterized by variability and stochas-ticity.Based on some biological features of the virus and the assumptions,the corresponding deterministic model is formulated,which takes into consideration the effect of vaccination.This deterministic model is extended to a stochastic framework by considering a new form of disturbance which makes it possible to simulate strong and significant fluctuations.The long-term behaviors of the virus are predicted by using stochastic differential equations with second-order multiplicative α-stable jumps.By developing the assumptions and employing the novel theoretical tools,the threshold parameter responsible for ergodicity(persistence)and extinction is provided.The theoretical results of the current study are validated by numerical simulations and parameters estimation is also performed.Moreover,we obtain the following new interesting findings:(a)in each class,the average time depends on the value ofα;(b)the second-order noise has an inverse effect on the spread of the virus;(c)the shapes of population densities at stationary level quickly changes at certain values of α.The last three conclusions can provide a solid research base for further investigation in the field of biological and ecological modeling.展开更多
Dear Editor,This letter addresses the challenge of forecasting the motion of real-world vessels over an extended period with a limited amount of available data.By employing stochastic differential equation(SDE)modelin...Dear Editor,This letter addresses the challenge of forecasting the motion of real-world vessels over an extended period with a limited amount of available data.By employing stochastic differential equation(SDE)modeling,we integrate both deterministic and stochastic components of the available information.Subsequently,we establish a recursive prediction methodology based on Bayes’rule to update the model state when new measurements are received.Furthermore,we develop a stochastic model tailored specifically to vessel dynamics and introduce an approximation method to tackle computational complexities.Finally,we present an application example and conduct a comparative experiment to validate the effectiveness and superiority of the proposed method.展开更多
Dear Editor,This letter investigates a partially-observed optimal control problem for backward stochastic differential delay equations(BSDDEs).By utilizing Girsanov’s theory and convex variational method,we obtain a ...Dear Editor,This letter investigates a partially-observed optimal control problem for backward stochastic differential delay equations(BSDDEs).By utilizing Girsanov’s theory and convex variational method,we obtain a maximum principle on the assumption that the state equation contains time delay and the control domain is convex.The adjoint processes can be represented as the solutions of certain time-advanced stochastic differential equations in finite-dimensional spaces.Linear backward stochastic differential equation(BSDE)was first introduced by Bismut in[1],while general BSDE was given by Pardoux and Peng[2].Since then,the theory of BSDEs developed rapidly.The corresponding optimal control problems,whose states are driven by BSDEs,have also been widely studied by some authors,see[3]-[5].展开更多
基金supported by the Natural Science Foundation of Shandong Province(Grant Nos.ZR2020MA032,ZR2022MA029)the National Natural Science Foundation of China(Grant No.72171133)the high-quality course for postgraduate education in Shandong Province《Intermediate Econometrics(Graded Teaching)》(SDYKC21137).
基金supported by the NSFC(12201557)the Foundation of Zhejiang Provincial Education Department,China(Y202249921).
文摘This work presents an advanced and detailed analysis of the mechanisms of hepatitis B virus(HBV)propagation in an environment characterized by variability and stochas-ticity.Based on some biological features of the virus and the assumptions,the corresponding deterministic model is formulated,which takes into consideration the effect of vaccination.This deterministic model is extended to a stochastic framework by considering a new form of disturbance which makes it possible to simulate strong and significant fluctuations.The long-term behaviors of the virus are predicted by using stochastic differential equations with second-order multiplicative α-stable jumps.By developing the assumptions and employing the novel theoretical tools,the threshold parameter responsible for ergodicity(persistence)and extinction is provided.The theoretical results of the current study are validated by numerical simulations and parameters estimation is also performed.Moreover,we obtain the following new interesting findings:(a)in each class,the average time depends on the value ofα;(b)the second-order noise has an inverse effect on the spread of the virus;(c)the shapes of population densities at stationary level quickly changes at certain values of α.The last three conclusions can provide a solid research base for further investigation in the field of biological and ecological modeling.
基金supported by the National Natural Science Foundation of China(62073019)the Key R&D Program of Hebei Province(22340301D)+1 种基金China Postdoctoral Science Foundation(2021M703021)Hebei Postdoctoral Science Foundation(B2021003031)。
文摘Dear Editor,This letter addresses the challenge of forecasting the motion of real-world vessels over an extended period with a limited amount of available data.By employing stochastic differential equation(SDE)modeling,we integrate both deterministic and stochastic components of the available information.Subsequently,we establish a recursive prediction methodology based on Bayes’rule to update the model state when new measurements are received.Furthermore,we develop a stochastic model tailored specifically to vessel dynamics and introduce an approximation method to tackle computational complexities.Finally,we present an application example and conduct a comparative experiment to validate the effectiveness and superiority of the proposed method.
文摘Dear Editor,This letter investigates a partially-observed optimal control problem for backward stochastic differential delay equations(BSDDEs).By utilizing Girsanov’s theory and convex variational method,we obtain a maximum principle on the assumption that the state equation contains time delay and the control domain is convex.The adjoint processes can be represented as the solutions of certain time-advanced stochastic differential equations in finite-dimensional spaces.Linear backward stochastic differential equation(BSDE)was first introduced by Bismut in[1],while general BSDE was given by Pardoux and Peng[2].Since then,the theory of BSDEs developed rapidly.The corresponding optimal control problems,whose states are driven by BSDEs,have also been widely studied by some authors,see[3]-[5].
