We consider a class of Markov processes with resettings, where at random times, the Markov processes are restarted from a predetermined point or a region. These processes are frequently applied in physics, chemistry, biology, economics, and in population dynamics. In this paper, we establish the local large deviation principle (LLDP) for the Wiener processes with random resettings, where the resettings occur at the arrival time of a Poisson process. Here, at each resetting time, a new resetting point is selected at random, according to a conditional distribution.

中文翻译：

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随机复位维纳过程的局部大偏差原理

我们考虑一类具有重置的马尔可夫过程，其中随机时间，马尔可夫过程从预定点或区域重新启动。这些过程经常应用于物理学、化学、生物学、经济学和人口动态。在本文中，我们为具有随机重置的维纳过程建立了局部大偏差原则（LLDP），其中重置发生在泊松过程的到达时间。这里，在每个复位时间，根据条件分布随机选择一个新的复位点。