q-期望值的稳定性准则
Stability criteria for q-expectation values
摘要：
在统计物理学中，最近一种特殊的平均值，称为q-期望值，已被广泛用于处理幂律分布的q-广义统计的上下文中。在这种情况下，q期望值自然出现。在最近已经表明，这种非线性功能是不稳定的，在一个非常强的稳定性的概念，因此，它是非常感兴趣的，以了解充分条件时，结果的q-期望是强大的小变化下的潜在分布函数。我们表明，合理的限制域的容许概率分布恢复一致连续的q-期望。可以给出容许变差大小的界。实际有用的定理估计的鲁棒性的q-期望值相对于小的变化进行了讨论。
英文摘要：
In statistical physics lately a specific kind of average, called the q-expectation value, has been extensively used in the context of q-generalized statistics dealing with distributions following power-laws. In this context q-expectation values appear naturally. After it has been recently shown that this non-linear functional is instable, under a very strong notion of stability, it is therefore of high interest to know sufficient conditions for when the results of q-expectations are robust under small variations of the underlying distribution function. We show that reasonable restrictions on the domain of admissible probability distributions restore uniform continuity for the q-expectation. Bounds on the size of admissible variations can be given. The practical usefulness of the theorems for estimating the robustness of the q-expectation value with respect to small variations is discussed.
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