收缩原理是大偏差理论的重要组成部分。
Contraction principle is an important constitution of large deviation theory.
遗憾的是，迄今为止经典的大偏差理论局限于线性情形，如线性概率，线性期望等。
Regretfully, so far the classic large deviation theory is confined to the linear case such as linear probability. linear expectation and so on.
因此，为了使大偏差理论在非线性领域得到更广泛的应用，本文研究了大偏差理论在非线性情形下的一些结果。
Thus, with the purpose of more extensive applications of large deviation theory in nonlinear field, this paper presents some results of large deviation in the nonlinear cases.
给出了能控制一切轻度重尾分布的分布族的两个新的等价条件，它们可以在大偏差理论及风险理论中发挥一定的作用。
We obtain two new equivalent conditions of one class of distributions which can dominate all lightly heavy-tailed distributions. They can turn out to be useful in large deviation and risk theory.
大偏差理论提供了一个很好的办法来计算小概率事件的概率，尽管这种事件发生的概率可能会很小，但是一旦发生将会产生巨大的影响。
Large deviation theory provides a good method to calculus the probability of rare event, which will have great impact once it happens although its probability may be very small.
众所周知，精细大偏差和风险理论是保险数学的两大主题。
It is well known that the precise large deviations and the risk theory are two of main objects in insurance mathematics.
结果表明，对比实验法的实验数据更接近理论值，最大偏差不超过1.5%。
Experiments show that the results of correlation method agree with those from Hay with a deviation of 1.5%.
进一步指出当台尺寸较小时，由于氧化剂在气相传送中也受到了限制，凹形台面氧化速率的实验值与理论值会出现较大偏差。
When the size of concave mesa was very small, the experimental data would deviate from the calculated data for the limitation of the gas transport.
该模型学习速率快，训练步骤少，逼近程度高，最大偏差不大于5％，为三相循环流化床蒸发器的传热计算提供了可靠的方法和理论基础；
Rapid learning speed, few training steps and high fidelity are advantages of the model. The maximal deviation is no more than 5%.
当用梁理论计算船体振动的高谐调特性时，理论计算值与实际试验量测值有较大偏差。这样，梁理论不能作为计算高协调振动的一个实际可用的方法。
When the beam theory was used to calculate ship hull vibration, greater discrepancies were found between theoretical calculations and actual measurements especially at higher-modes.
当用梁理论计算船体振动的高谐调特性时，理论计算值与实际试验量测值有较大偏差。这样，梁理论不能作为计算高协调振动的一个实际可用的方法。
When the beam theory was used to calculate ship hull vibration, greater discrepancies were found between theoretical calculations and actual measurements especially at higher-modes.
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