Limit theorems for cloning algorithms
Limit theorems for cloning algorithms
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DOI：
10.1016/j.spa.2021.04.007
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发表时间：
2019-02
影响因子：
1.4
通讯作者：
Letizia Angeli;S. Grosskinsky;A. M. Johansen
中科院分区：
文献类型：
--
作者：
Letizia Angeli;S. Grosskinsky;A. M. Johansen
随机过程可加路径泛函的大偏差引起了广泛的研究兴趣，特别是在随机粒子系统和统计物理的背景下。基于通过克隆稀有事件轨迹的重要性抽样，已经开发出高效的数值‘克隆’算法来估计定标累积量发生函数。到目前为止，研究这些算法在连续时间内的收敛性质的尝试只导致了特定情况下的部分结果。借鉴粒子滤波和序贯蒙特卡罗方法的研究成果，我们首次建立了一种全面而严格的方法来解决克隆算法的系统误差和随机误差在连续时间内的界问题。为此，我们发展了一种方法来比较不同的算法，为特定类别的可观测，基于随机过程的鞅特征。与以往的方法相比，我们的结果适用于紧致状态空间上的一大类跳跃过程，并且不涉及任何时间离散化。这提供了一个健壮和严格的框架，也可以用来评估和提高算法的效率。
Large deviations for additive path functionals of stochastic processes have attracted significant research interest, in particular in the context of stochastic particle systems and statistical physics. Efficient numerical ‘cloning’ algorithms have been developed to estimate the scaled cumulant generating function, based on importance sampling via cloning of rare event trajectories. So far, attempts to study the convergence properties of these algorithms in continuous time have led to only partial results for particular cases. Adapting previous results from the literature of particle filters and sequential Monte Carlo methods, we establish a first comprehensive and fully rigorous approach to bound systematic and random errors of cloning algorithms in continuous time. To this end we develop a method to compare different algorithms for particular classes of observables, based on the martingale characterization of stochastic processes. Our results apply to a large class of jump processes on compact state space, and do not involve any time discretization in contrast to previous approaches. This provides a robust and rigorous framework that can also be used to evaluate and improve the efficiency of algorithms.