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Decomposing correlated random walks on common and counter movements

机译：分解相关随机散步，符合常见和计数器

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摘要

Random walk is one of the most classical models in probability theory which has got extensive applications in many areas and is still of great interest in practice. For those problems that require modelling two random walks on lattice, correlation of the random walks is non-ignorable. This paper presents a new method to study the dependency structure of two generally correlated random walks. By introducing a change-of-time process, two correlated random walks can be decomposed into sum/difference of two independent random walks with time change, where the two independent random walks present respectively the common movements and counter movements of the original random walks. A sufficient and necessary condition is given for the mutual independence of the change-of-time process and the two independent random walks. For the prospective applications of the decomposition method in theory and practice, we consider the calculations of the characteristic functions for Markovian and non-Markovian random walks and an empirical example in futures trading is given. (C) 2019 Elsevier B.V. All rights reserved.
机译：随机步行是概率理论中最古典的模型之一，在许多领域拥有广泛的应用，并且对实践仍然很兴趣。对于需要建模两个随机散步的那些问题，随机散步的相关性是非忽略的。本文介绍了一种研究两种大致相关随机散步的依赖结构的新方法。通过引入时间变化的过程，两个相关的随机散步可以分解成两个独立随机散步的总和/差异，其中两个独立的随机散步分别存在原始随机散步的公共运动和计数器运动。给出了足够的条件，用于相互独立的变化过程和两个独立的随机行走。对于分解方法在理论与实践的前瞻性应用中，我们考虑了马尔可维亚和非马尔可维亚随机行走的特征功能的计算，并给出了期货交易的经验例子。 （c）2019年Elsevier B.V.保留所有权利。

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