论文标题
马尔可夫过程中幸存的轨迹的巨大偏差
Large deviations for surviving trajectories of general Markov processes
论文作者
论文摘要
本文的目的是确保Gärtner-ellis定理的条件以评估经验度量。我们表明，可以有效地应用确保与准平台分布的收敛性的最新条件。以此为例，即使在评估结束时该过程并未灭绝，我们也能够证明较大的偏差结果。这些大偏差结果适用的领域是由可以证明上述准平台结果的惩罚范围隐含的。我们提出了一种将受控偏差范围与可允许的惩罚范围联系起来的方法。从大偏差的这些结果中推导了中心限制定理。作为一个应用程序，我们考虑了$ r^d $的无效域上连续时间流程的经验度量和跳跃。该模型的灵感来自于人口适应不断变化的环境。跳跃使过程可以面对确定性动态，从而导致高消光区。
The purpose of this paper is to ensure the conditions of Gärtner-Ellis Theorem for evaluations of the empirical measure. We show that up-to-date conditions for ensuring the convergence to a quasi-stationary distribution can be applied efficiently. By this mean, we are able to prove Large Deviation results even with a conditioning that the process is not extinct at the end of the evaluation. The domain on which these Large Deviation results apply is implicitly given by the range of penalization for which one can prove the above-mentioned results of quasi-stationarity. We propose a way to relate the range of controlled deviations to the range of admissible penalization. Central Limit Theorems are deduced from these results of Large Deviations. As an application, we consider the empirical measure of position and jumps of a continuous-time process on aunbounded domain of $R^d$. This model is inspired by the adaptation of a population to a changing environment. Jumps makes it possible for the process to face a deterministic dynamics leading to high extinction areas.
