In this paper, we consider a hyper-exponential jump-diffusion model with a constant dividend barrier. Explicit solutions for the Laplace transform of the ruin time, and the Gerber- Shiu function are obtained via marti...In this paper, we consider a hyper-exponential jump-diffusion model with a constant dividend barrier. Explicit solutions for the Laplace transform of the ruin time, and the Gerber- Shiu function are obtained via martingale stopping.展开更多
In this paper,accelerated saddle point dynamics is proposed for distributed resource allocation over a multi-agent network,which enables a hyper-exponential convergence rate.Specifically,an inertial fast-slow dynamica...In this paper,accelerated saddle point dynamics is proposed for distributed resource allocation over a multi-agent network,which enables a hyper-exponential convergence rate.Specifically,an inertial fast-slow dynamical system with vanishing damping is introduced,based on which the distributed saddle point algorithm is designed.The dual variables are updated in two time scales,i.e.,the fast manifold and the slow manifold.In the fast manifold,the consensus of the Lagrangian multipliers and the tracking of the constraints are pursued by the consensus protocol.In the slow manifold,the updating of the Lagrangian multipliers is accelerated by inertial terms.Hyper-exponential stability is defined to characterize a faster convergence of our proposed algorithm in comparison with conventional primal-dual algorithms for distributed resource allocation.The simulation of the application in the energy dispatch problem verifies the result,which demonstrates the fast convergence of the proposed saddle point dynamics.展开更多
In this paper we shall characterize the large deviation principles(abbreviated to LDP) of Donsker-Varadhan of a Markov process both for the weak convergence topology and for theτ- topology,by means of a hyper-exponen...In this paper we shall characterize the large deviation principles(abbreviated to LDP) of Donsker-Varadhan of a Markov process both for the weak convergence topology and for theτ- topology,by means of a hyper-exponential recurrence property.A Lyapunov criterion for this type of recurrence property is presented.These results are applied to countable Markov chains,unidimensional diffusions,elliptic or hypoelliptic diffusions on Riemannian manifolds.Several counter-examples are equally presented.展开更多
基金Supported by the Natural Science Foundation of Jiangsu Province(BK20130260)the National Natural Science Foundation of China(11301369)the Postdoctoral Science Foundation of China(2013M540371)
文摘In this paper, we consider a hyper-exponential jump-diffusion model with a constant dividend barrier. Explicit solutions for the Laplace transform of the ruin time, and the Gerber- Shiu function are obtained via martingale stopping.
基金supported by the National Natural Science Foundation of China(61773172)supported in part by the Australian Research Council(DP200101197,DE210100274)。
文摘In this paper,accelerated saddle point dynamics is proposed for distributed resource allocation over a multi-agent network,which enables a hyper-exponential convergence rate.Specifically,an inertial fast-slow dynamical system with vanishing damping is introduced,based on which the distributed saddle point algorithm is designed.The dual variables are updated in two time scales,i.e.,the fast manifold and the slow manifold.In the fast manifold,the consensus of the Lagrangian multipliers and the tracking of the constraints are pursued by the consensus protocol.In the slow manifold,the updating of the Lagrangian multipliers is accelerated by inertial terms.Hyper-exponential stability is defined to characterize a faster convergence of our proposed algorithm in comparison with conventional primal-dual algorithms for distributed resource allocation.The simulation of the application in the energy dispatch problem verifies the result,which demonstrates the fast convergence of the proposed saddle point dynamics.
基金This work is partially supported by the NSF of China and the Foundation of Y.D.Fok.
文摘In this paper we shall characterize the large deviation principles(abbreviated to LDP) of Donsker-Varadhan of a Markov process both for the weak convergence topology and for theτ- topology,by means of a hyper-exponential recurrence property.A Lyapunov criterion for this type of recurrence property is presented.These results are applied to countable Markov chains,unidimensional diffusions,elliptic or hypoelliptic diffusions on Riemannian manifolds.Several counter-examples are equally presented.
