It is well known that the precise large deviations and the risk theory are two of main objects in insurance mathematics.

众所周知，精细大偏差和风险理论是保险数学的两大主题。

youdao

Furthermore, we establish a large deviations principle for the family of invariant measures as the perturbations tend to zero.

还进一步建立了当扰动趋于零时，关于这族不变测度的大偏差原理。

youdao

By traditional method of large deviations, we obtain the logarithmic asymptotic for the probabilities and large deviation principle for the corresponding measures.

利用经典大偏差的方法，在一定的条件下，得到了相应概率的对数渐近式及测度族的大偏差原理。

youdao

The times that it has materially deviated have been associated with large deviations in monetary supply.

FORBES: Gold Moving In Anticipation of QE3 -- But Be Forewarned

In complex systems, the slightest variation in initial conditions can create large deviations in future system conditions over time and not necessarily in predictable ways.

FORBES: The Case for Climate-Change Alarmism

Varadhan, New York University, for his work in probability theory, especially his work on large deviations from expected random behavior which has revolutionized this field of study during the second half of the 20th century, and become a cornerstone of both pure and applied probability.

WHITEHOUSE: President Obama Honors the Country��s Top Innovators and Scientists | The White House