In this paper,we prove a general law of the iterated logarithm (LIL) for independent non-identically distributed B-valued random variables.As an interesting application,we obtain the law of the iterated logarithm for ...In this paper,we prove a general law of the iterated logarithm (LIL) for independent non-identically distributed B-valued random variables.As an interesting application,we obtain the law of the iterated logarithm for the empirical covariance of Hilbertian autoregressive processes.展开更多
We show sharp bounds for probabilities of large deviations for sums of independent random variables satisfying Bernstein's condition. One such bound is very close to the tail of the standard Gaussian law in certai...We show sharp bounds for probabilities of large deviations for sums of independent random variables satisfying Bernstein's condition. One such bound is very close to the tail of the standard Gaussian law in certain case; other bounds improve the inequalities of Bennett and Hoeffding by adding missing factors in the spirit of Talagrand(1995). We also complete Talagrand's inequality by giving a lower bound of the same form, leading to an equality. As a consequence, we obtain large deviation expansions similar to those of Cram′er(1938),Bahadur-Rao(1960) and Sakhanenko(1991). We also show that our bound can be used to improve a recent inequality of Pinelis(2014).展开更多
To analyze the effect of basic variable on failure probability in reliability analysis,a moment-independent importance measure of the basic random variable is proposed,and its properties are analyzed and verified.Base...To analyze the effect of basic variable on failure probability in reliability analysis,a moment-independent importance measure of the basic random variable is proposed,and its properties are analyzed and verified.Based on this work,the importance measure of the basic variable on the failure probability is compared with that on the distribution density of the response.By use of the probability density evolution method,a solution is established to solve two importance measures,which can efficiently avoid the difficulty in solving the importance measures.Some numerical examples and engineering examples are used to demonstrate the proposed importance measure on the failure probability and that on the distribution density of the response.The results show that the proposed importance measure can effectively describe the effect of the basic variable on the failure probability from the distribution density of the basic variable.Additionally,the results show that the established solution on the probability density evolution is efficient for the importance measures.展开更多
This paper deals with random Taylor series whose coefficients consist of independent random variables {X n} with the property: αE 1/2 {|X n| 2}≤E{|X n|}<∞, E{X n}=0 (n ) for some positive cons...This paper deals with random Taylor series whose coefficients consist of independent random variables {X n} with the property: αE 1/2 {|X n| 2}≤E{|X n|}<∞, E{X n}=0 (n ) for some positive constant α. The convergence, growth, and value distribution of the series are investigated.展开更多
RECENTLY, a number of papers have been published concerning the asymptotic independentproperties of V X<sub>i</sub> and sum from 1 X<sub>i</sub> of weakly dependent stationary sequence {X<su...RECENTLY, a number of papers have been published concerning the asymptotic independentproperties of V X<sub>i</sub> and sum from 1 X<sub>i</sub> of weakly dependent stationary sequence {X<sub>i</sub>}.In this letter, let {X<sub>i</sub>} be a standard normal sequence of random variables with zero meanand unit variance and write r<sub>ij</sub>=cov（X<sub>i</sub>, X<sub>j</sub>）.展开更多
We show large deviation expansions for sums of independent and bounded from above random variables. Our moderate deviation expansions are similar to those of Cram′er(1938), Bahadur and Ranga Rao(1960), and Sakhanenko...We show large deviation expansions for sums of independent and bounded from above random variables. Our moderate deviation expansions are similar to those of Cram′er(1938), Bahadur and Ranga Rao(1960), and Sakhanenko(1991). In particular, our results extend Talagrand's inequality from bounded random variables to random variables having finite(2 + δ)-th moments, where δ∈(0, 1]. As a consequence,we obtain an improvement of Hoeffding's inequality. Applications to linear regression, self-normalized large deviations and t-statistic are also discussed.展开更多
Let(Xn)n≥1 be a sequence of independent identically distributed(i.i.d.) positive random variables with EX1 = μ,Var(X1) = σ2.In the present paper,we establish the moderate deviations principle for the products of pa...Let(Xn)n≥1 be a sequence of independent identically distributed(i.i.d.) positive random variables with EX1 = μ,Var(X1) = σ2.In the present paper,we establish the moderate deviations principle for the products of partial sums(πnk=1Sk/n!μn)1/(γbn√(2n))1where γ = σ/μ denotes the coefficient of variation and(bn) is the moderate deviations scale.展开更多
基金the National Natural Science Foundation of China (Grant Nos.10671176,10771192)
文摘In this paper,we prove a general law of the iterated logarithm (LIL) for independent non-identically distributed B-valued random variables.As an interesting application,we obtain the law of the iterated logarithm for the empirical covariance of Hilbertian autoregressive processes.
基金supported by the Post-Graduate Study Abroad Program sponsored by China Scholarship CouncilNational Natural Science Foundation of China(Grant Nos.11171044 and11401590)
文摘We show sharp bounds for probabilities of large deviations for sums of independent random variables satisfying Bernstein's condition. One such bound is very close to the tail of the standard Gaussian law in certain case; other bounds improve the inequalities of Bennett and Hoeffding by adding missing factors in the spirit of Talagrand(1995). We also complete Talagrand's inequality by giving a lower bound of the same form, leading to an equality. As a consequence, we obtain large deviation expansions similar to those of Cram′er(1938),Bahadur-Rao(1960) and Sakhanenko(1991). We also show that our bound can be used to improve a recent inequality of Pinelis(2014).
基金supported by the National Natural Science Foundation of China (Grant Nos NSFC1057211, 50875213)New Century Excellent Talents in University of China (Grant No NCET-05-0868)+2 种基金Aviation Science Foundation of China (Grant No 2007ZA53012)National High Technology Research and Development Program of China (Grant No 2007AA04Z401)the Important National Science & Technology Specific Projects (Grant No 2009ZX04014-015-03)
文摘To analyze the effect of basic variable on failure probability in reliability analysis,a moment-independent importance measure of the basic random variable is proposed,and its properties are analyzed and verified.Based on this work,the importance measure of the basic variable on the failure probability is compared with that on the distribution density of the response.By use of the probability density evolution method,a solution is established to solve two importance measures,which can efficiently avoid the difficulty in solving the importance measures.Some numerical examples and engineering examples are used to demonstrate the proposed importance measure on the failure probability and that on the distribution density of the response.The results show that the proposed importance measure can effectively describe the effect of the basic variable on the failure probability from the distribution density of the basic variable.Additionally,the results show that the established solution on the probability density evolution is efficient for the importance measures.
文摘This paper deals with random Taylor series whose coefficients consist of independent random variables {X n} with the property: αE 1/2 {|X n| 2}≤E{|X n|}<∞, E{X n}=0 (n ) for some positive constant α. The convergence, growth, and value distribution of the series are investigated.
文摘RECENTLY, a number of papers have been published concerning the asymptotic independentproperties of V X<sub>i</sub> and sum from 1 X<sub>i</sub> of weakly dependent stationary sequence {X<sub>i</sub>}.In this letter, let {X<sub>i</sub>} be a standard normal sequence of random variables with zero meanand unit variance and write r<sub>ij</sub>=cov（X<sub>i</sub>, X<sub>j</sub>）.
基金supported by National Natural Science Foundation of China (Grant Nos. 11601375 and 11626250)
文摘We show large deviation expansions for sums of independent and bounded from above random variables. Our moderate deviation expansions are similar to those of Cram′er(1938), Bahadur and Ranga Rao(1960), and Sakhanenko(1991). In particular, our results extend Talagrand's inequality from bounded random variables to random variables having finite(2 + δ)-th moments, where δ∈(0, 1]. As a consequence,we obtain an improvement of Hoeffding's inequality. Applications to linear regression, self-normalized large deviations and t-statistic are also discussed.
基金supported by National Natural Science Foundation of China (Grant No.11001077)
文摘Let(Xn)n≥1 be a sequence of independent identically distributed(i.i.d.) positive random variables with EX1 = μ,Var(X1) = σ2.In the present paper,we establish the moderate deviations principle for the products of partial sums(πnk=1Sk/n!μn)1/(γbn√(2n))1where γ = σ/μ denotes the coefficient of variation and(bn) is the moderate deviations scale.
