In this paper, we use sample average approximation with adaptive multiple importance sampling to explore moderate deviations for the optimal values. Utilizing the moderate deviation principle for martingale difference...In this paper, we use sample average approximation with adaptive multiple importance sampling to explore moderate deviations for the optimal values. Utilizing the moderate deviation principle for martingale differences and an appropriate Delta method, we establish a moderate deviation principle for the optimal value. Moreover, for a functional form of stochastic programming, we obtain a functional moderate deviation principle for its optimal value.展开更多
M-negatively associated random variables, which generalizes the classical one of negatively associated random variables and includes m-dependent sequences as its particular case, are introduced and studied. Large devi...M-negatively associated random variables, which generalizes the classical one of negatively associated random variables and includes m-dependent sequences as its particular case, are introduced and studied. Large deviation principles and moderate deviation upper bounds for stationary m-negatively associated random variables are proved. Kolmogorov-type and Marcinkiewicz-type strong laws of large numbers as well as the three series theorem for m-negatively associated random variables are also given.展开更多
Let fn be a non-parametric kernel density estimator based on a kernel function K. and a sequence of independent and identically distributed random variables taking values in R. The goal of this article is to prove mod...Let fn be a non-parametric kernel density estimator based on a kernel function K. and a sequence of independent and identically distributed random variables taking values in R. The goal of this article is to prove moderate deviations and large deviations for the statistic sup ｜fn（x） - fn（-x） ｜.展开更多
We study moderate deviations for estimators of the drift parameter of the fractional Ornstein-Uhlenbeck process. Two moderate deviation principles are obtained.
The authors consider the moderate deviations of hydrodynamic limit for Ginzburg-Landau models. The moderate deviation principle of hydrodynamic limit for a specific Ginzburg-Landau model is obtained and an explicit fo...The authors consider the moderate deviations of hydrodynamic limit for Ginzburg-Landau models. The moderate deviation principle of hydrodynamic limit for a specific Ginzburg-Landau model is obtained and an explicit formula of the rate function is derived.展开更多
In this article, we obtain the large deviations and moderate deviations for negatively dependent （ND） and non-identically distributed random variables defined on （-∞, ＋∞）. The results show that for some non-ide...In this article, we obtain the large deviations and moderate deviations for negatively dependent （ND） and non-identically distributed random variables defined on （-∞, ＋∞）. The results show that for some non-identical random variables, precise large deviations and moderate deviations remain insensitive to negative dependence structure.展开更多
In this paper we prove a central limit theorem and a moderate deviation principle for a class of semilinear stochastic partial differential equations, which contain the stochastic Burgers’ equation and the stochastic...In this paper we prove a central limit theorem and a moderate deviation principle for a class of semilinear stochastic partial differential equations, which contain the stochastic Burgers’ equation and the stochastic reaction-diffusion equation. The weak convergence method plays an important role.展开更多
By the method of change measures, the moderate deviations for the Bessel clock ∫t0ds/xs（v） is studied, where （Xt（v）, t ≥0） is a squared Bessel process with index v 〉 0. Xs The rate function can be given expl...By the method of change measures, the moderate deviations for the Bessel clock ∫t0ds/xs（v） is studied, where （Xt（v）, t ≥0） is a squared Bessel process with index v 〉 0. Xs The rate function can be given explicitly. Furthermore, the functional moderate deviations for the Bessel clock are obtained.展开更多
Suppose that Y1 , Y2 , , Yn are independent and identically distributed n observations from convolution model Y = X ＋ ε, where X is an unobserved random variable with unknown density f X,and ε is the measurement er...Suppose that Y1 , Y2 , , Yn are independent and identically distributed n observations from convolution model Y = X ＋ ε, where X is an unobserved random variable with unknown density f X,and ε is the measurement error with a known density function. Set f n （ x ）to be a nonparametric kernel density estimator of f X,and the pointwise and uniform moderate deviations of statistic sup x∈ R ｜ f n （ x ） f n（ x） ｜are given by Gine and Guillou＇s exponential inequality.展开更多
We study the asymptotics tot the statistic of chi-square in type Ⅱ error. By the contraction principle, the large deviations and moderate deviations are obtained, and the rate function of moderate deviations can be c...We study the asymptotics tot the statistic of chi-square in type Ⅱ error. By the contraction principle, the large deviations and moderate deviations are obtained, and the rate function of moderate deviations can be calculated explicitly which is a squared function.展开更多
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
In this paper,we study asymptotic properties of the approximated maximum likelihood estimator(MLE)for the drift coefficient in an Ornstein-Uhlenbeck process with discrete observations.By the change of measure method a...In this paper,we study asymptotic properties of the approximated maximum likelihood estimator(MLE)for the drift coefficient in an Ornstein-Uhlenbeck process with discrete observations.By the change of measure method and asymptotic analysis technique,we establish an exponential nonuniform Berry-Esseen bound of the approximated MLE.Then,the Cramér-type moderate deviation can be obtained.As applications,the global and local powers for the hypothesis test are shown to approach one at exponential rates.Simulation experiments are conducted to confirm the theoretical results.展开更多
In this paper,we study asymptotic behavior of small perturbation for path-distribution dependent stochastic differential equations driven simultaneously by a fractional Brownian motion with Hurst parameter H∈(1/2,1)a...In this paper,we study asymptotic behavior of small perturbation for path-distribution dependent stochastic differential equations driven simultaneously by a fractional Brownian motion with Hurst parameter H∈(1/2,1)and a standard Brownian motion.We establish large and moderate deviation principles by utilising the weak convergence approach.展开更多
Let{X,X_(n);n≥1}be a sequence of i.i.d.non-degenerate real-valued random variables with EX^(2)<∞.Let S_(n)=∑_(i=1)^(n)X_(i),n≥1.Let g(·):[0,∞)→[0,∞)be a nondecreasing regularly varying function with in...Let{X,X_(n);n≥1}be a sequence of i.i.d.non-degenerate real-valued random variables with EX^(2)<∞.Let S_(n)=∑_(i=1)^(n)X_(i),n≥1.Let g(·):[0,∞)→[0,∞)be a nondecreasing regularly varying function with indexρ≥0 and limt→∞g(t)=∞.Letμ=EX andσ^(2)=E(X−μ)^(2).In this paper,on the scale g(log n),we obtain precise asymptotic estimates for the probabilities of moderate deviations of the form log P(S_(n)−nμ>x√ng(log n)),log P(S_(n)−nμ<−x√ng(log n)),and log P(|S_(n)−nμ|>x√ng(log n))for all x>0.Unlike those known results in the literature,the moderate deviation results established in this paper depend on both the variance and the asymptotic behavior of the tail distribution of X.展开更多
We study a multivariate linear Hawkes process with random marks.In this paper,we establish that a central limit theorem,a moderate deviation principle and an upper bound of large deviation for multivariate marked Hawk...We study a multivariate linear Hawkes process with random marks.In this paper,we establish that a central limit theorem,a moderate deviation principle and an upper bound of large deviation for multivariate marked Hawkes processes hold.展开更多
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...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
The present paper first shows that, without any dependent structure assumptions for a sequence of random variables, the refined results of the complete convergence for the sequence is equivalent to the corresponding c...The present paper first shows that, without any dependent structure assumptions for a sequence of random variables, the refined results of the complete convergence for the sequence is equivalent to the corresponding complete moment convergence of the sequence. Then this paper investigates the convergence rates and refined convergence rates （or complete moment convergence） for probabilities of moderate deviations of moving average processes. The results in this paper extend and generalize some well-known results.展开更多
Let {Xn;n≥ 1} be a sequence of independent non-negative random variables with common distribution function F having extended regularly varying tail and finite mean μ = E（X1） and let {N（t）; t ≥0} be a random pro...Let {Xn;n≥ 1} be a sequence of independent non-negative random variables with common distribution function F having extended regularly varying tail and finite mean μ = E（X1） and let {N（t）; t ≥0} be a random process taking non-negative integer values with finite mean λ（t） = E（N（t）） and independent of {Xn; n ≥1}. In this paper, asymptotic expressions of P（（X1 ＋… ＋XN（t）） -λ（t）μ 〉 x） uniformly for x ∈[γb（t）, ∞） are obtained, where γ〉 0 and b（t） can be taken to be a positive function with limt→∞ b（t）/λ（t） = 0.展开更多
We prove a moderate deviation principle for a super-Brownian motion with immigration of all dimensions, and consequently fill the gap between the central limit theorem and large deviation principle.
We study deviation inequalities for some quadratic Wiener functionals and moderate deviations for parameter estimators in a linear stochastic differential equation model.Firstly,we give some estimates for Laplace inte...We study deviation inequalities for some quadratic Wiener functionals and moderate deviations for parameter estimators in a linear stochastic differential equation model.Firstly,we give some estimates for Laplace integrals of the quadratic Wiener functionals by calculating the eigenvalues of the associated HilbertSchmidt operators.Then applying the estimates,we establish deviation inequalities for the quadratic functionals and moderate deviation principles for the parameter estimators.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.12071175)。
文摘In this paper, we use sample average approximation with adaptive multiple importance sampling to explore moderate deviations for the optimal values. Utilizing the moderate deviation principle for martingale differences and an appropriate Delta method, we establish a moderate deviation principle for the optimal value. Moreover, for a functional form of stochastic programming, we obtain a functional moderate deviation principle for its optimal value.
基金Partly supported by the National Natural Science Foundation of China and the Ministry of Education of ChinaPartly supported by the Science and Technology Research Item of Hubei Provincial Department of Education,Jiaghan University
文摘M-negatively associated random variables, which generalizes the classical one of negatively associated random variables and includes m-dependent sequences as its particular case, are introduced and studied. Large deviation principles and moderate deviation upper bounds for stationary m-negatively associated random variables are proved. Kolmogorov-type and Marcinkiewicz-type strong laws of large numbers as well as the three series theorem for m-negatively associated random variables are also given.
基金Research supported by the National Natural Science Foundation of China (10271091)
文摘Let fn be a non-parametric kernel density estimator based on a kernel function K. and a sequence of independent and identically distributed random variables taking values in R. The goal of this article is to prove moderate deviations and large deviations for the statistic sup ｜fn（x） - fn（-x） ｜.
基金Research supported by the National Natural Science Foundation of China (10571139)
文摘We study moderate deviations for estimators of the drift parameter of the fractional Ornstein-Uhlenbeck process. Two moderate deviation principles are obtained.
基金Supported by the National Natural Science Foundation of China (10271091)
文摘The authors consider the moderate deviations of hydrodynamic limit for Ginzburg-Landau models. The moderate deviation principle of hydrodynamic limit for a specific Ginzburg-Landau model is obtained and an explicit formula of the rate function is derived.
基金supported by the Youth Foundation of Hubei Province Department of Education of China (Q200710002)
文摘In this article, we obtain the large deviations and moderate deviations for negatively dependent （ND） and non-identically distributed random variables defined on （-∞, ＋∞）. The results show that for some non-identical random variables, precise large deviations and moderate deviations remain insensitive to negative dependence structure.
基金supported by NSFF(17BTJ034)The research of WANG was supported by NSFC(11871382,11771161).
文摘In this paper we prove a central limit theorem and a moderate deviation principle for a class of semilinear stochastic partial differential equations, which contain the stochastic Burgers’ equation and the stochastic reaction-diffusion equation. The weak convergence method plays an important role.
基金Research supported by the National Natural Science Foundation of China(10871153)funded by the Revitalization Project of Zhongnan University of Economics and Law
文摘By the method of change measures, the moderate deviations for the Bessel clock ∫t0ds/xs（v） is studied, where （Xt（v）, t ≥0） is a squared Bessel process with index v 〉 0. Xs The rate function can be given explicitly. Furthermore, the functional moderate deviations for the Bessel clock are obtained.
文摘Suppose that Y1 , Y2 , , Yn are independent and identically distributed n observations from convolution model Y = X ＋ ε, where X is an unobserved random variable with unknown density f X,and ε is the measurement error with a known density function. Set f n （ x ）to be a nonparametric kernel density estimator of f X,and the pointwise and uniform moderate deviations of statistic sup x∈ R ｜ f n （ x ） f n（ x） ｜are given by Gine and Guillou＇s exponential inequality.
基金the National Natural Science Foundation of China (10571139)
文摘We study the asymptotics tot the statistic of chi-square in type Ⅱ error. By the contraction principle, the large deviations and moderate deviations are obtained, and the rate function of moderate deviations can be calculated explicitly which is a squared function.
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 by the National Natural Science Foundation of China(Grant No.12471146)the Natural Science Foundation of Jiangsu Province of China(Grant No.BK20231435)。
文摘In this paper,we study asymptotic properties of the approximated maximum likelihood estimator(MLE)for the drift coefficient in an Ornstein-Uhlenbeck process with discrete observations.By the change of measure method and asymptotic analysis technique,we establish an exponential nonuniform Berry-Esseen bound of the approximated MLE.Then,the Cramér-type moderate deviation can be obtained.As applications,the global and local powers for the hypothesis test are shown to approach one at exponential rates.Simulation experiments are conducted to confirm the theoretical results.
基金supported by the National Natural Science Foundation of China(Grant No.12571160)supported in part by the UIC Start-up Research Fund(Grant No.UICR0700072-24)。
文摘In this paper,we study asymptotic behavior of small perturbation for path-distribution dependent stochastic differential equations driven simultaneously by a fractional Brownian motion with Hurst parameter H∈(1/2,1)and a standard Brownian motion.We establish large and moderate deviation principles by utilising the weak convergence approach.
基金Supported by Natural Sciences and Engineering Research Council of Canada(Grant No.RGPIN-2019-06065)National Natural Science Foundation of China(Grant No.NSFC-11971154)。
文摘Let{X,X_(n);n≥1}be a sequence of i.i.d.non-degenerate real-valued random variables with EX^(2)<∞.Let S_(n)=∑_(i=1)^(n)X_(i),n≥1.Let g(·):[0,∞)→[0,∞)be a nondecreasing regularly varying function with indexρ≥0 and limt→∞g(t)=∞.Letμ=EX andσ^(2)=E(X−μ)^(2).In this paper,on the scale g(log n),we obtain precise asymptotic estimates for the probabilities of moderate deviations of the form log P(S_(n)−nμ>x√ng(log n)),log P(S_(n)−nμ<−x√ng(log n)),and log P(|S_(n)−nμ|>x√ng(log n))for all x>0.Unlike those known results in the literature,the moderate deviation results established in this paper depend on both the variance and the asymptotic behavior of the tail distribution of X.
基金supported by Doctoral Scientific Research Starting Foundation of Jingdezhen Ceramic University(No.102/01003002031)Academic Achievement Re-cultivation Projects of Jingdezhen Ceramic University(No.215/20506341 and No.215/20506277).
文摘We study a multivariate linear Hawkes process with random marks.In this paper,we establish that a central limit theorem,a moderate deviation principle and an upper bound of large deviation for multivariate marked Hawkes processes hold.
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National Natural Science Foundation of China (Grant No.60574002)MASCOS grant from Australian Research CouncilNational Natural Science Foundation of China (Grant No.70671018)
文摘The present paper first shows that, without any dependent structure assumptions for a sequence of random variables, the refined results of the complete convergence for the sequence is equivalent to the corresponding complete moment convergence of the sequence. Then this paper investigates the convergence rates and refined convergence rates （or complete moment convergence） for probabilities of moderate deviations of moving average processes. The results in this paper extend and generalize some well-known results.
基金Research supported by NSFC(No.10271091,10571139)
文摘Let {Xn;n≥ 1} be a sequence of independent non-negative random variables with common distribution function F having extended regularly varying tail and finite mean μ = E（X1） and let {N（t）; t ≥0} be a random process taking non-negative integer values with finite mean λ（t） = E（N（t）） and independent of {Xn; n ≥1}. In this paper, asymptotic expressions of P（（X1 ＋… ＋XN（t）） -λ（t）μ 〉 x） uniformly for x ∈[γb（t）, ∞） are obtained, where γ〉 0 and b（t） can be taken to be a positive function with limt→∞ b（t）/λ（t） = 0.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.10071008 and 10121101).
文摘We prove a moderate deviation principle for a super-Brownian motion with immigration of all dimensions, and consequently fill the gap between the central limit theorem and large deviation principle.
基金National Natural Science Foundation of China(Grant Nos. 11171262,11571262 and 11101210)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20130141110076)+1 种基金the Fundamental Research Funds for the Central Universities(Grant No.NS2015074)China Postdoctoral Science Foundation(Grant Nos.2013M531341 and 2016T90450)
文摘We study deviation inequalities for some quadratic Wiener functionals and moderate deviations for parameter estimators in a linear stochastic differential equation model.Firstly,we give some estimates for Laplace integrals of the quadratic Wiener functionals by calculating the eigenvalues of the associated HilbertSchmidt operators.Then applying the estimates,we establish deviation inequalities for the quadratic functionals and moderate deviation principles for the parameter estimators.
