Record numbers are important statistics in random walk models. Their deviation principles are unknown as far as we know. In this article, we provide the asymptotic probabilities of large and moderate deviations for the number of weak records in one-dimensional symmetric simple random walks.
The project was supported by the National Natural Science Foundation of China (Grant No. 11671145), the Natural Science Foundation of Shanghai (Grant No. 16ZR1409700) and the Program of China Scholarships Council (Grant No. 201806145024). The project was supported in part by the Science and Technology Commission of Shanghai Municipality(Grant No. 18dz2271000).