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.
