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Freidlin-Wentzell’s Large Deviations for Stochastic Evolution Equations with Poisson Jumps 被引量:1
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作者 Huiyan Zhao Siyan Xu 《Advances in Pure Mathematics》 2016年第10期676-694,共20页
We establish a Freidlin-Wentzell’s large deviation principle for general stochastic evolution equations with Poisson jumps and small multiplicative noises by using weak convergence method.
关键词 stochastic Evolution Equation Poisson Jumps freidlin-wentzell’s large deviation Weak Convergence Method
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Sharp large deviation results for sums of independent random variables 被引量:1
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作者 FAN XieQuan GRAMA Ion LIU QuanSheng 《Science China Mathematics》 SCIE CSCD 2015年第9期1939-1958,共20页
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
关键词 Bernstein’s inequality sharp large deviations Cramér large deviations expansion of BahadurRao sums of independent random variabl
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Sharp large deviations for sums of bounded from above random variables
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作者 FAN XieQuan 《Science China Mathematics》 SCIE CSCD 2017年第12期2465-2480,共16页
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
关键词 sharp large deviations Cram′er large deviations Talagrand’s inequality Hoeffding’s inequality sums of independent random variables
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Quasi Sure Large Deviation for Increments of Fractional Brownian Motion in H¨older Norm
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作者 Jie XU Yun Min ZHU Ji Cheng LIU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2015年第6期913-920,共8页
In this paper, we first prove Schilder's theorem in H?lder norm (0 ≤ α 〈1) with respect to Cr,p-capacity. Then, based on this result, we further prove a sharpening of large deviation principle for increments of... In this paper, we first prove Schilder's theorem in H?lder norm (0 ≤ α 〈1) with respect to Cr,p-capacity. Then, based on this result, we further prove a sharpening of large deviation principle for increments of fractional Brownian motion for Cr,p-capacity in the stronger topology. 展开更多
关键词 schilder's theorem large deviations fractional Brownian motion Cr p-capacity
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Self-normalization:Taming a wild population in a heavy-tailed world 被引量:2
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作者 SHAO Qi-man ZHOU Wen-xin 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2017年第3期253-269,共17页
The past two decades have witnessed the active development of a rich probability theory of Studentized statistics or self-normalized processes, typified by Student’s t-statistic as introduced by W. S. Gosset more tha... The past two decades have witnessed the active development of a rich probability theory of Studentized statistics or self-normalized processes, typified by Student’s t-statistic as introduced by W. S. Gosset more than a century ago, and their applications to statistical problems in high dimensions, including feature selection and ranking, large-scale multiple testing and sparse, high dimensional signal detection. Many of these applications rely on the robustness property of Studentization/self-normalization against heavy-tailed sampling distributions. This paper gives an overview of the salient progress of self-normalized limit theory, from Student’s t-statistic to more general Studentized nonlinear statistics. Prototypical examples include Studentized one- and two-sample U-statistics. Furthermore, we go beyond independence and glimpse some very recent advances in self-normalized moderate deviations under dependence. 展开更多
关键词 Berry-Esseen inequality Hotelling’s T <sup>2sup>-statistic large deviation moderate deviation sELF-NORMALIZATION student’s t-statistic U-sTATIsTIC
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重尾分布S下延迟索赔风险过程的精细大偏差 被引量:1
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作者 肖鸿民 赵弘宇 王占魁 《河南师范大学学报(自然科学版)》 CAS 北大核心 2020年第3期1-5,F0002,共6页
讨论了一类非经典风险模型(延迟索赔风险模型)的极限性质.假设主索赔额序列和延迟索赔额序列均是同分布的重尾随机变量序列.在索赔额属于S族的条件下,利用鞅论得到了损失过程的部分和与随机和的精细大偏差.
关键词 延迟索赔 s 停时 精细大偏差
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次指数随机变量列的精致大偏差
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作者 杨洋 王岳宝 《广西师范大学学报(自然科学版)》 CAS 北大核心 2006年第2期36-39,共4页
得到了独立同次指数分布随机变量的精致大偏差结果,取消了现有的类似结果中q(t)最终单调趋于0的条件,同时稍微加强了下述条件:m in(α,β)>N,对某个N>2,并且得到了以负相协随机变量列的更新过程为随机脚标的类似结果。
关键词 s s^*族 大偏差
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关于广义几何分布的强偏差定理
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作者 王学武 《经济数学》 2007年第3期300-306,共7页
利用对数似然比作为一类整值随机变量序列相对于独立随机变量序列的偏差度量,在限定对数似然比的给定样本空间的子集上,建立并证明一类整值随机变量序列的强偏差定理,作为推论得到了此类分布的独立随机变量序列的若干强大数定律.
关键词 强偏差 广义几何分布 对数似然比 A.s.收敛 强大数定律
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