The solution of nonlinear parabolic equation arising from population dynamics with boundary and initial value are established by the finite difference method,as well as it denotes the unique generalized global solution.
This paper is the first attempt to investigate the risk probability criterion in semi-Markov decision processes with loss rates. The goal is to find an optimal policy with the minimum risk probability that the total l...This paper is the first attempt to investigate the risk probability criterion in semi-Markov decision processes with loss rates. The goal is to find an optimal policy with the minimum risk probability that the total loss incurred during a first passage time to some target set exceeds a loss level. First, we establish the optimality equation via a successive approximation technique, and show that the value function is the unique solution to the optimality equation. Second, we give suitable conditions, under which we prove the existence of optimal policies and develop an algorithm for computing ?-optimal policies. Finally, we apply our main results to a business system.展开更多
The authors study a linear inverse problem with a biological interpretation,which is modelled by a Fredholm integral equation of the first kind, where the kernel is represented by step functions. Based on different as...The authors study a linear inverse problem with a biological interpretation,which is modelled by a Fredholm integral equation of the first kind, where the kernel is represented by step functions. Based on different assumptions, identifiability, stability and reconstruction results are obtained.展开更多
文摘The solution of nonlinear parabolic equation arising from population dynamics with boundary and initial value are established by the finite difference method,as well as it denotes the unique generalized global solution.
基金supported by National Natural Science Foundation of China(Grant Nos.61374067 and 11471341)
文摘This paper is the first attempt to investigate the risk probability criterion in semi-Markov decision processes with loss rates. The goal is to find an optimal policy with the minimum risk probability that the total loss incurred during a first passage time to some target set exceeds a loss level. First, we establish the optimality equation via a successive approximation technique, and show that the value function is the unique solution to the optimality equation. Second, we give suitable conditions, under which we prove the existence of optimal policies and develop an algorithm for computing ?-optimal policies. Finally, we apply our main results to a business system.
基金partially supported by the Basal-CMM Project,the Fondecyt Grant(No.1130317,1111012,1140773)"Agence Nationale de la Recherche" Project CISIFS(No.ANR-09-BLAN-0213-02)partially supported by ECOS-CONICYT C13E05 and Basal-CeBiB
文摘The authors study a linear inverse problem with a biological interpretation,which is modelled by a Fredholm integral equation of the first kind, where the kernel is represented by step functions. Based on different assumptions, identifiability, stability and reconstruction results are obtained.
