Applying the Markov renewal theorem, it is shown that certain reasonable conditions of the QBD process lead to the geometric decay of the tail probabilities as the level goes to infinity.

通过对QBD过程某些条件的限定，应用马尔可夫更新定理，得出在一定合理的条件下，当水平趋于无穷时的尾概率的几何衰变。

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We discover that, under certain conditions, the three precise large-deviation probabilities with different centering numbers are equivalent to each other.

同时发现，在一定的条件下，带有不同中心化常数的三个精致大偏差概率是彼此等价的。

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In order to reveal peoples selecting probabilities of certain actions under the general expectation of return, the mathematic model of behavior probability is put forward.

为了研究人们在某种行为回报的普遍预期下选择该行为的概率，建立了行为概率的数学模型。

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The interpretation, which is the most popular explanation of the bizarre quantum world among physicists, suggests that quantum mechanics does not describe the physical world directly but merely talks about probabilities of certain outcomes.

ECONOMIST: A quantum physicist's long-awaited second book

The best it can do is talk in terms of risk and of probabilities, the likelihood that an event of a certain magnitude might occur at some point in the future.

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