This paper studies the moderate deviations of real-valued extended negatively dependent(END) random variables with consistently varying tails.The moderate deviations of partial sums are first given.The results are the...This paper studies the moderate deviations of real-valued extended negatively dependent(END) random variables with consistently varying tails.The moderate deviations of partial sums are first given.The results are then used to establish the necessary and sufficient conditions for the moderate deviations of random sums under certain circumstances.展开更多
We consider a branching random walk in random environments, where the particles are reproduced as a branching process with a random environment (in time), and move independently as a random walk on ? with a random env...We consider a branching random walk in random environments, where the particles are reproduced as a branching process with a random environment (in time), and move independently as a random walk on ? with a random environment (in locations). We obtain the asymptotic properties on the position of the rightmost particle at time n, revealing a phase transition phenomenon of the system.展开更多
Let(Zn)be a supercritical branching process with immigration in an independent and identically distributed random environment.Under necessary moment conditions,we show the exact convergence rate in the central limit t...Let(Zn)be a supercritical branching process with immigration in an independent and identically distributed random environment.Under necessary moment conditions,we show the exact convergence rate in the central limit theorem on log Zn and establish the corresponding local limit theorem by using the moments of the natural submartingale and the convergence rates of its logarithm.By similar approach and with the help of a change of measure,we also present the so-called integrolocal theorem and integral large deviation theorem to characterize the precise asymptotics of the upper large deviations.展开更多
We consider a supercritical branching process （Zn） in an independent and identically distributed random environment ξ, and present some recent results on the asymptotic properties of the limit variable W of the nat...We consider a supercritical branching process （Zn） in an independent and identically distributed random environment ξ, and present some recent results on the asymptotic properties of the limit variable W of the natural martingale Wn = Zn/E[Zn｜ξ], the convergence rates of W - Wn （by considering the convergence in law with a suitable norming, the almost sure convergence, the convergence in Lp, and the convergence in probability）, and limit theorems （such as central limit theorems, moderate and large deviations principles） on （log Zn）.展开更多
We consider a branching random walk on N with a random environment in time （denoted by ξ）. Let Zn be the counting measure of particles of generation n, and let Zn（t） be its Laplace transform. We show the converge...We consider a branching random walk on N with a random environment in time （denoted by ξ）. Let Zn be the counting measure of particles of generation n, and let Zn（t） be its Laplace transform. We show the convergence of the free energy n-llog Zn（t）, large deviation principles, and central limit theorems for the sequence of measures {Zn}, and a necessary and sufficient condition for the existence of moments of the limit of the martingale Zn（t）/E[Zn（t）ξ].展开更多
农业干旱监测问题对农业生产具有重要影响,因此精确监测农业干旱具有现实意义。该研究基于MOD16A2全球蒸散产品,计算作物缺水指数(Crop Water Stress Index,CWSI),结合地表温度、植被指数、降水量以及土壤湿度等多源遥感数据为自变量,以...农业干旱监测问题对农业生产具有重要影响,因此精确监测农业干旱具有现实意义。该研究基于MOD16A2全球蒸散产品,计算作物缺水指数(Crop Water Stress Index,CWSI),结合地表温度、植被指数、降水量以及土壤湿度等多源遥感数据为自变量,以3个月时间尺度的标准化降水蒸散指数(Standardized Precipitation Evapotranspiration Index,SPEI-3)为因变量,基于偏差校正随机森林算法构建山东省2000—2019年作物生长季(4—10月)的偏差校正随机森林干旱状况指数(Bias-corrected Random Forest Drought Condition Index,BRF-DCI)。并分析CWSI对于构建山东省农业干旱监测模型的影响。结果表明:加入CWSI后,所提出的BRF-DCI指数与SPEI-3观测指数的决定系数为0.72~0.85,优于未加入CWSI之前;加入CWSI后提高了干旱等级监测的准确率;BRF-DCI指数能较好地拟合各月份的SPEI-3指数,决定系数均在0.94以上;BRF-DCI指数能够准确反映山东省典型干旱年的干旱情况,有效监测山东省农业干旱情况。该研究对山东省农业旱情监测及旱灾防御具有较大的应用潜力。展开更多
The vertices of an infinite locally finite tree T are labelled by a collection of i.i.d. real random variables {Xσ}σ∈T which defines a tree indexed walk Xr. We introduce and study theoscillations of the walk:where ...The vertices of an infinite locally finite tree T are labelled by a collection of i.i.d. real random variables {Xσ}σ∈T which defines a tree indexed walk Xr. We introduce and study theoscillations of the walk:where Φ(n) is an increasing sequence of positive numbers. We prove that for each $ belonging to a certain class of sequences of different orders, there are ξ 's depending on Φ such that 0 < OSCΦ(ξ) <∞. Exact Hausdorff dimension of the set of such ξ's is calculated. An application is given to study the local variation of Brownian motion. A general limsup deviation problem on trees is also studied.展开更多
Let X, X1, X2,... be i.i.d, random variables with mean zero and positive, finite variance σ^2, and set Sn = X1 ＋... ＋ Xn, n≥1. The author proves that, if EX^2I{｜X｜≥t} = 0（（log log t）^-1） as t→∞, then for ...Let X, X1, X2,... be i.i.d, random variables with mean zero and positive, finite variance σ^2, and set Sn = X1 ＋... ＋ Xn, n≥1. The author proves that, if EX^2I{｜X｜≥t} = 0（（log log t）^-1） as t→∞, then for any a〉-1 and b〉 -1,lim ε↑1/√1＋a（1/√1＋a-ε）b＋1 ∑n=1^∞（logn）^a（loglogn）^b/nP{max κ≤n｜Sκ｜≤√σ^2π^2n/8loglogn（ε＋an）}=4/π（1/2（1＋a）^3/2）^b＋1 Г（b＋1）,whenever an = o（1/log log n）. The author obtains the sufficient and necessary conditions for this kind of results to hold.展开更多
Moderate deviations for the quenched mean of the super-Brownian motion with random immigration are proved for 3≤d≤6, which fills in the gap between central limit theorem(CLT)and large deviation principle(LDP).
基金supported by National Natural Science Foundation of China(Grant No.10571139)the Research Foundation of Education Bureau of Hubei Province,China (Grant No.Q200710002)
文摘This paper studies the moderate deviations of real-valued extended negatively dependent(END) random variables with consistently varying tails.The moderate deviations of partial sums are first given.The results are then used to establish the necessary and sufficient conditions for the moderate deviations of random sums under certain circumstances.
基金the National Natural Science Foundation of China (Grant Nos. 10271020,10471012)SRF for ROCS, SEM (Grant No. [2005]564)
文摘We consider a branching random walk in random environments, where the particles are reproduced as a branching process with a random environment (in time), and move independently as a random walk on ? with a random environment (in locations). We obtain the asymptotic properties on the position of the rightmost particle at time n, revealing a phase transition phenomenon of the system.
基金Supported by Shandong Provincial Natural Science Foundation(Grant No.ZR2021MA085)National Natural Science Foundation of China(Grant No.11971063)。
文摘Let(Zn)be a supercritical branching process with immigration in an independent and identically distributed random environment.Under necessary moment conditions,we show the exact convergence rate in the central limit theorem on log Zn and establish the corresponding local limit theorem by using the moments of the natural submartingale and the convergence rates of its logarithm.By similar approach and with the help of a change of measure,we also present the so-called integrolocal theorem and integral large deviation theorem to characterize the precise asymptotics of the upper large deviations.
基金Acknowledgements This work was partially supported by the National Natural Science Foundation of China （Grant Nos. 11171044, 11101039） and the Natural Science Foundation of Hunan Province （Grant No. 11JJ2001）.
文摘We consider a supercritical branching process （Zn） in an independent and identically distributed random environment ξ, and present some recent results on the asymptotic properties of the limit variable W of the natural martingale Wn = Zn/E[Zn｜ξ], the convergence rates of W - Wn （by considering the convergence in law with a suitable norming, the almost sure convergence, the convergence in Lp, and the convergence in probability）, and limit theorems （such as central limit theorems, moderate and large deviations principles） on （log Zn）.
基金Acknowledgements The authors would like to thank the anonymous referees for valuable comments and remarks. This work was partially supported by the Natural Scientific Research Innovation Foundation in Harbin Institute of Technology （HIT. NSRIF. 2015102）, the National Natural Science Foundation of China （Grant Nos. 11171044, 11101039）, and by the Natural Science Foundation of Hunan Province （Grant No. 11JJ2001）.
文摘We consider a branching random walk on N with a random environment in time （denoted by ξ）. Let Zn be the counting measure of particles of generation n, and let Zn（t） be its Laplace transform. We show the convergence of the free energy n-llog Zn（t）, large deviation principles, and central limit theorems for the sequence of measures {Zn}, and a necessary and sufficient condition for the existence of moments of the limit of the martingale Zn（t）/E[Zn（t）ξ].
文摘The vertices of an infinite locally finite tree T are labelled by a collection of i.i.d. real random variables {Xσ}σ∈T which defines a tree indexed walk Xr. We introduce and study theoscillations of the walk:where Φ(n) is an increasing sequence of positive numbers. We prove that for each $ belonging to a certain class of sequences of different orders, there are ξ 's depending on Φ such that 0 < OSCΦ(ξ) <∞. Exact Hausdorff dimension of the set of such ξ's is calculated. An application is given to study the local variation of Brownian motion. A general limsup deviation problem on trees is also studied.
基金National Natural Science Foundation of China (No.10471126)
文摘Let X, X1, X2,... be i.i.d, random variables with mean zero and positive, finite variance σ^2, and set Sn = X1 ＋... ＋ Xn, n≥1. The author proves that, if EX^2I{｜X｜≥t} = 0（（log log t）^-1） as t→∞, then for any a〉-1 and b〉 -1,lim ε↑1/√1＋a（1/√1＋a-ε）b＋1 ∑n=1^∞（logn）^a（loglogn）^b/nP{max κ≤n｜Sκ｜≤√σ^2π^2n/8loglogn（ε＋an）}=4/π（1/2（1＋a）^3/2）^b＋1 Г（b＋1）,whenever an = o（1/log log n）. The author obtains the sufficient and necessary conditions for this kind of results to hold.
基金the Program for New Century Excellent Talents in University (Grant No. 05-0143)the National Natural Science Foundation of China (Grant No. 10721091)
文摘Moderate deviations for the quenched mean of the super-Brownian motion with random immigration are proved for 3≤d≤6, which fills in the gap between central limit theorem(CLT)and large deviation principle(LDP).
