Large deviations estimates for Poisson processes estimate the logarithm of rare events associated to a Poisson process which has more and more jump which are smaller and smaller. In stochastic analysis, they are valid...Large deviations estimates for Poisson processes estimate the logarithm of rare events associated to a Poisson process which has more and more jump which are smaller and smaller. In stochastic analysis, they are valid on the whole path space. Asoociated to this jump process is a Markov semi-group. We translate in semi group theory the proof of Wentzel-Freidlin for these estimates by translating in semi-group theory some basical tools of stochastic analysis as the exponential martingales of stochastic analysis. These Wentzel-Freidlin estimates （upper-bound） are only true for the semi-group.展开更多
Consider a family of probability measures {vξ} on a bounded open region D C Rd with a smooth boundary and a positive parameter set {βξ}, all indexed by ξ∈δD. For any starting point inside D, we run a diffusion u...Consider a family of probability measures {vξ} on a bounded open region D C Rd with a smooth boundary and a positive parameter set {βξ}, all indexed by ξ∈δD. For any starting point inside D, we run a diffusion until it first exits D, at which time it stays at the exit point ξ for an independent exponential holding time with rate βξ and then leaves ξ by a jump into D according to the distribution ξ. Once the process jumps inside, it starts the diffusion afresh. The same evolution is repeated independently each time the process jumped into the domain. The resulting Markov process is called diffusion with holding and jumping boundary （DHJ）, which is not reversible due to the jumping. In this paper we provide a study of DHJ on its generator, stationary distribution and the speed of convergence.展开更多
The authors introduce concepts of even and odd additive functionals and prove that an even martingale continuous additive functional of a symmetric Markov process vanishes identically.A representation for symmetric s...The authors introduce concepts of even and odd additive functionals and prove that an even martingale continuous additive functional of a symmetric Markov process vanishes identically.A representation for symmetric super-martingale multiplicative functionals are also given.展开更多
文摘Large deviations estimates for Poisson processes estimate the logarithm of rare events associated to a Poisson process which has more and more jump which are smaller and smaller. In stochastic analysis, they are valid on the whole path space. Asoociated to this jump process is a Markov semi-group. We translate in semi group theory the proof of Wentzel-Freidlin for these estimates by translating in semi-group theory some basical tools of stochastic analysis as the exponential martingales of stochastic analysis. These Wentzel-Freidlin estimates （upper-bound） are only true for the semi-group.
基金supported by National Natural Science Foundation of China(Grant No.11101433)the Fundamental Research Funds for the Central South University(Grant No.2011QNZT105)+1 种基金Doctorial Dissertation Program of Hunan Province(Grant No.YB2011B009)US National Science Foundation (Grant Nos.AMC-SS-0706713,DMS-0805929,NSFC-6398100 and CAS-2008DP173182)
文摘Consider a family of probability measures {vξ} on a bounded open region D C Rd with a smooth boundary and a positive parameter set {βξ}, all indexed by ξ∈δD. For any starting point inside D, we run a diffusion until it first exits D, at which time it stays at the exit point ξ for an independent exponential holding time with rate βξ and then leaves ξ by a jump into D according to the distribution ξ. Once the process jumps inside, it starts the diffusion afresh. The same evolution is repeated independently each time the process jumped into the domain. The resulting Markov process is called diffusion with holding and jumping boundary （DHJ）, which is not reversible due to the jumping. In this paper we provide a study of DHJ on its generator, stationary distribution and the speed of convergence.
基金Project supported by the National Natural Science Foundation of China.
文摘The authors introduce concepts of even and odd additive functionals and prove that an even martingale continuous additive functional of a symmetric Markov process vanishes identically.A representation for symmetric super-martingale multiplicative functionals are also given.
