We establish an invariance principle and a large deviation principle for a biased random walk ${\text{RW}}_\lambda$ with $\lambda\in [0,1)$ on $\mathbb{Z}^d$ . The scaling limit in the invariance principle is not a d-dimensional Brownian motion. For the large deviation principle, its rate function is different from that of a drifted random walk, as may be expected, though the reflected biased random walk evolves like the drifted random walk in the interior of the first quadrant and almost surely visits coordinate planes finitely many times.

中文翻译：

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有偏随机游走的不变原理和大偏差原理

我们为有偏随机游走建立了不变性原理和大偏差原理${\text{RW}}_\lambda$和$\lambda\in [0,1)$在$\mathbb{Z}^d$. 不变原理中的缩放限制不是d维布朗运动。对于大偏差原理，它的速率函数不同于漂移随机游走的速率函数，正如可以预料的那样，尽管反射的有偏随机游走像第一象限内部的漂移随机游走一样演变，并且几乎可以肯定地有限地访问坐标平面多次。