We are interested in the convergence rates of the submartingale Wn=Z_(n)/Π_(n)to its limit W,where(Π_(n))is the usually used norming sequence and(Z_(n))is a supercritical branching process with immigration(Y_(n))in ...We are interested in the convergence rates of the submartingale Wn=Z_(n)/Π_(n)to its limit W,where(Π_(n))is the usually used norming sequence and(Z_(n))is a supercritical branching process with immigration(Y_(n))in a stationary and ergodic environmentξ.Under suitable conditions,we establish the following central limit theorems and results about the rates of convergence in probability or in law:(i)W-W_(n) with suitable normalization converges to the normal law N(0,1),and similar results also hold for W_(n+k)-W_(n) for each fixed k∈N^(*);(ii)for a branching process with immigration in a finite state random environment,if W_(1) has a finite exponential moment,then so does W,and the decay rate of P(|W-W_(n)|>ε)is supergeometric;(iii)there are normalizing constants an(ξ)(that we calculate explicitly)such that a_(n)(ξ)(W-W_(n))converges in law to a mixture of the Gaussian law.展开更多
The action of wind on the sea surface plays an important role in the noise generation mechanism.Sea surface wind speed can be estimated accurately provided there is an accurate understanding of the relationship betwee...The action of wind on the sea surface plays an important role in the noise generation mechanism.Sea surface wind speed can be estimated accurately provided there is an accurate understanding of the relationship between the ocean ambient noise and wind speed.Many measurements and analyses of the wind dependence of ambient noise have been conducted.The approximate empirical rule given by Wenz[1]states that in the frequency band between 0.5and 5 kHz,the ambient sea-noise spectrum levels decrease展开更多
We propose a feasible scheme of generating multipartite entanglement with the dipole induced transparency （D/T） effect in indirectly coupled dipole-microcavity systems. It is shown that the transmission spectrum is ...We propose a feasible scheme of generating multipartite entanglement with the dipole induced transparency （D/T） effect in indirectly coupled dipole-microcavity systems. It is shown that the transmission spectrum is closely related with the interference of dipole-microcavity systems, and we can generate different classes of multi- partite entanglement, e.g., the Greenberger-Horne-Zeilinger state, the W state, and the Dicke state, of the di- pole emitters just by choosing an appropriate frequency of the incident photon. Benefiting from the DIT effect, the schemes may work in the bad or low-Q cavity regime only if the large Purcell factor of the dipole-microcavity system is fulfilled, and they are also insensitive to experimental noise, which may be feasible with present acces- sible technology.展开更多
For diffusion processes,we extend various two-sided exit identities to the situation when the process is only observed at arrival times of an independent Poisson process.The results are expressed in terms of solutions...For diffusion processes,we extend various two-sided exit identities to the situation when the process is only observed at arrival times of an independent Poisson process.The results are expressed in terms of solutions to the differential equations associated with the diffusions generators.展开更多
基金supported by the National Natural Science Foundation of China(11571052,11731012)the Hunan Provincial Natural Science Foundation of China(2018JJ2417)the Open Fund of Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering(2018MMAEZD02)。
文摘We are interested in the convergence rates of the submartingale Wn=Z_(n)/Π_(n)to its limit W,where(Π_(n))is the usually used norming sequence and(Z_(n))is a supercritical branching process with immigration(Y_(n))in a stationary and ergodic environmentξ.Under suitable conditions,we establish the following central limit theorems and results about the rates of convergence in probability or in law:(i)W-W_(n) with suitable normalization converges to the normal law N(0,1),and similar results also hold for W_(n+k)-W_(n) for each fixed k∈N^(*);(ii)for a branching process with immigration in a finite state random environment,if W_(1) has a finite exponential moment,then so does W,and the decay rate of P(|W-W_(n)|>ε)is supergeometric;(iii)there are normalizing constants an(ξ)(that we calculate explicitly)such that a_(n)(ξ)(W-W_(n))converges in law to a mixture of the Gaussian law.
基金supported by the National Natural Science Foundation of China(Grant Nos.11434012,41561144006,and 11404366)
文摘The action of wind on the sea surface plays an important role in the noise generation mechanism.Sea surface wind speed can be estimated accurately provided there is an accurate understanding of the relationship between the ocean ambient noise and wind speed.Many measurements and analyses of the wind dependence of ambient noise have been conducted.The approximate empirical rule given by Wenz[1]states that in the frequency band between 0.5and 5 kHz,the ambient sea-noise spectrum levels decrease
基金supported by the National Natural Science Foundation of China(Nos.11405052,11504104,and11704115)the Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control(No.QSQC1409)
文摘We propose a feasible scheme of generating multipartite entanglement with the dipole induced transparency （D/T） effect in indirectly coupled dipole-microcavity systems. It is shown that the transmission spectrum is closely related with the interference of dipole-microcavity systems, and we can generate different classes of multi- partite entanglement, e.g., the Greenberger-Horne-Zeilinger state, the W state, and the Dicke state, of the di- pole emitters just by choosing an appropriate frequency of the incident photon. Benefiting from the DIT effect, the schemes may work in the bad or low-Q cavity regime only if the large Purcell factor of the dipole-microcavity system is fulfilled, and they are also insensitive to experimental noise, which may be feasible with present acces- sible technology.
基金This work was supported in part by the National Natural Science Foundation of China(Grant Nos.11571052,11731012)the Natural Science Foundation of Hunan Province(Grant Nos.2018JJ2417,2019JJ50405)+3 种基金the Outstanding Youth Foundation of Hunan Province Department of Education(Grant No.18B401)the China Scholarship Council(Grant No.201808430239)Open Fund of Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering(Grant No.2018MMAEZD02)the Doctoral Scientific Research Project of Hunan University of Arts and Science.
文摘For diffusion processes,we extend various two-sided exit identities to the situation when the process is only observed at arrival times of an independent Poisson process.The results are expressed in terms of solutions to the differential equations associated with the diffusions generators.
