In this paper, we propose a stochastic version of the Hawking–Penrose black hole model. We describe the dynamics of the stochastic model as a continuous-time Markov jump process of quanta out and in the black hole. The average of the random process satisfies the deterministic picture accepted in the physical literature. Assuming that the number of quanta is finite the proposed Markov process consists of two componentes: the number of the quanta in the black hole and the amount of the quanta outside.

The stochastic representation allows us to apply large deviation theory to study the asymptotics of probabilities of rare events when the number of quanta grows to infinity. The theory provides explicitly the rate functional for the process. Its infimum over the set of all trajectories leading to large emission event is attained on the most probable trajectory. This trajectory is a solution of a highly nonlinear Hamiltonian system of equations. Under the condition of stationarity of the fraction of quanta in the black hole, we found the most probable trajectory corresponding to a large emission event.

在本文中，我们提出了Hawking-Penrose黑洞模型的随机版本。我们将随机模型的动力学描述为量子出入黑洞的连续时间马尔可夫跳跃过程。随机过程的平均值满足物理文献中接受的确定性图景。假设量子数量是有限的，建议的马尔可夫过程由两个部分组成：黑洞中的量子数量和外面的量子数量。

随机表示允许我们应用大偏差理论来研究当量子数量增长到无穷大时稀有事件概率的渐近性。该理论明确提供了该过程的速率函数。在最可能的轨迹上实现了导致所有大型排放事件的所有轨迹集的最小量。该轨迹是高度非线性哈密顿方程组的一种解决方案。在黑洞中量子份额平稳的条件下，我们发现了与大发射事件相对应的最可能的轨迹。