Invariance principle for non-homogeneous random walks (Q2423454)

As to spatially homogeneous random walks, a well-known result is the Donsker invariance principle, which describes the scaling limit for the class of homogeneous random walks whose increments have zero mean and positive-definite covariance in terms of Brownian motion on \(\mathbb{R}^d\). This paper studies scaling limits of the non-homogeneous random walks introduced in [the first author et al., Adv. Appl. Probab. 48, No. A, 99--118 (2016; Zbl 1426.60095)]. These non-homogeneous random walks may be recurrent in any dimension. The paper studies the limit process in several aspects and presents a sequence of interesting results.