We study Berry-Esseen bounds and Cramér-type moderate deviations of a jump-type Cox-Ingersoll-Ross(CIR)process driven by a standard Wiener process and a subordinator.In the sub critical case,we obtain the best Be...We study Berry-Esseen bounds and Cramér-type moderate deviations of a jump-type Cox-Ingersoll-Ross(CIR)process driven by a standard Wiener process and a subordinator.In the sub critical case,we obtain the best Berry-Esseen bound of the sample mean and the MLE of the growth rate if the Lévy measure of the subordinator has finite third order moment.Under the Cramér condition,we establish the Cramér-type moderate deviations of the MLE of the growth rate.We first derive a Berry-Esseen bound,a deviation inequality and the Cramér-type moderate deviations for the sample mean of the CIR process by analyzing the asymptotic behaviors of the characteristic function and the moment generating function of the sample mean.Then we analyze a type of additive functional of the jump-type CIR process and use a transformation to study the Berry-Esseen bound and the Cramér-type moderate deviations for the MLE of the growth rate.展开更多
We obtain upper and lower bounds of the exit times from balls of a jump-type symmetric Markov process. The proofs are delivered separately. The upper bounds are obtained by using the Levy system corresponding to the p...We obtain upper and lower bounds of the exit times from balls of a jump-type symmetric Markov process. The proofs are delivered separately. The upper bounds are obtained by using the Levy system corresponding to the process, while the precise expression of the （L^2-）generator of the Dirichlet form associated with the process is used to obtain the lower bounds.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.11971361,12371275)。
文摘We study Berry-Esseen bounds and Cramér-type moderate deviations of a jump-type Cox-Ingersoll-Ross(CIR)process driven by a standard Wiener process and a subordinator.In the sub critical case,we obtain the best Berry-Esseen bound of the sample mean and the MLE of the growth rate if the Lévy measure of the subordinator has finite third order moment.Under the Cramér condition,we establish the Cramér-type moderate deviations of the MLE of the growth rate.We first derive a Berry-Esseen bound,a deviation inequality and the Cramér-type moderate deviations for the sample mean of the CIR process by analyzing the asymptotic behaviors of the characteristic function and the moment generating function of the sample mean.Then we analyze a type of additive functional of the jump-type CIR process and use a transformation to study the Berry-Esseen bound and the Cramér-type moderate deviations for the MLE of the growth rate.
基金Supported partly by Grand-in-Aid for Scientific Research (C)
文摘We obtain upper and lower bounds of the exit times from balls of a jump-type symmetric Markov process. The proofs are delivered separately. The upper bounds are obtained by using the Levy system corresponding to the process, while the precise expression of the （L^2-）generator of the Dirichlet form associated with the process is used to obtain the lower bounds.
