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1.
We study the moderate deviation probability of the position of the rightmost particle in a branching Brownian motion and obtain its moderate deviation function. Firstly, Chauvin and Rouault studied the large deviation probability for the rightmost position in a branching Brownian motion. Recently, Derrida and Shiconsidered lower deviation for the same model. By contrast, Our main result is more extensive.  相似文献   

2.
Deciding whether a given pattern is over- or under-represented according to a given background model is a key question in computational biology. Such a decision is usually made by computing some p-values reflecting the “exceptionality” of a pattern in a given sequence or set of sequences. In the simplest cases (short and simple patterns, simple background model, small number of sequences), an exact p-value can be computed with a tractable complexity. The realistic cases are in general too complicated to get such an exact p-value. Approximations are thus proposed (Gaussian, Poisson, Large deviation approximations). These approximations are applicable under some conditions: Gaussian approximations are valid in the central domain while Poisson and Large deviation approximations are valid for rare events. In the present paper, we prove a large deviation approximation to the double strands counting problem that refers to a counting of a given pattern in a set of sequences that arise from both strands of the genome. In that case, dependencies between a sequence and its reverse complement cannot be neglected. They are captured here for a Bernoulli model from general combinatorial properties of the pattern. A large deviation result is also provided for a set of small sequences.  相似文献   

3.
宫晓莉  熊熊 《运筹与管理》2019,28(5):124-133
基于非参数统计方法,利用考虑金融资产价格跳跃和杠杆效应的时点波动估计方法修正已实现阈值幂变差,构造甄别跳跃的检验统计量,对金融资产价格中的随机波动、有限活跃跳跃和无限活跃跳跃等问题进行综合研究。为同时吸收波动率的异方差集聚效应和收益率的非对称效应,对原有的已实现波动率异质自回归预测模型进行拓展,将非对称的异质性自回归模型的误差项设定为GARCH模型,以考察跳跃波动序列与连续波动序列之间的复杂关系。利用沪深股指高频数据进行实证研究,包括进行跳跃识别,跳跃活动程度检验和波动率预测效果对比。研究结果表明,沪深股市同时存在布朗运动成分、有限活跃跳跃和无限活跃跳跃成分,其中连续路径方差占主体。同时,收益和波动间的杠杆效应显著,无论短期还是长期,连续波动和跳跃波动对波动率的预测均具有显著影响,同时考虑股价的跳跃、波动和杠杆效应因素有助于更准确地刻画资产价格动态过程。  相似文献   

4.
In this article, several scan statistics are discussed for detecting a local change in variance for one dimensional normal data. When the length of the scanning window is known, a fixed window scan statistic based on moving sum of squares is proposed. Two approximations for the distribution of this scan statistic are investigated. When the length of the scanning window is unknown, a variable window scan statistic based on a generalized likelihood ratio test and a multiple window minimum P-value scan statistic are proposed for detecting the local change in variance. For a moderate or large shift in variance, numerical results indicate that both the variable and multiple window scan statistics perform well. For large data sets, considering the detection power and computing efficiency, the multiple window scan statistic is recommended.  相似文献   

5.
We are concerned with SIR epidemics in a random environment on complete graphs, where edges are assigned with i.i.d. weights. Our main results give large and moderate deviation principles of sample paths of this model. Our results generalize large and moderate deviation principles of the classic SIR models given by E. Pardoux and B. Samegni-Kepgnou [J. Appl. Probab., 2017, 54: 905-920] and X. F. Xue [Stochastic Process. Appl., 2019, 140: 49-80].  相似文献   

6.
In this work, we obtain a large and moderate deviation principle for the law of the maximum of a random Dyck path. Our result extends the results of Chung (1976), Kennedy (1976) and Khorunzhiy and Marckert (2009).  相似文献   

7.
苗雨 《数学杂志》2005,25(4):358-360
在某种正则条件下,对Bayes估计尾概率收敛速度问题进行了讨论。利用似然理论方法得到了Bayes估计的中偏差下界,从而改善了Bahadur型的收敛结果。  相似文献   

8.
9.
本文讨论了多参数指数族分布一类特殊的单边假设的MRST,导出了两类错误概率的大偏差近似。作为特例,我们研究了方差未知时正态均值单边假设的MRST,得到了显著性水平和功效的渐近近似公式。  相似文献   

10.
In this note, we consider the large and moderate deviation principle of the estimators of the integrated covariance of two-dimensional diffusion processes when they are observed only at discrete times in a synchronous manner. The proof is extremely simple. It is essentially an application of the contraction principle for the results given in the case of the volatility by Djellout et al. (1999).  相似文献   

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