Large and moderate deviations for record numbers in some non–nearest neighbor random walks

The deviation principles of record numbers in random walk models have not been completely investigated, especially for the non-nearest neighbor cases. In this paper, we derive asymptotic probabilities large and moderate deviations number "weak records"(or "ladder points") two kinds one-dimensional walks. proofs depend only on direct analysis We illustrate that traditional method analyzing local time Brownian motions, which is often adopted simple walks, would lead to wrong conjectures our