2025/06/01 by Chi, Zhiyi, Pozdnyakov, Vladimir
#60G42 #60J10 #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.2506.00990
Assume that letters (from a finite alphabet) in a text form a Markov chain. We track two distinct words, U and D. A gambler gains 1 point for each occurrence of U (including overlapping occurrences) and loses 1 point for each occurrence of D (also including overlapping occurrences). We determine the probability of gaining A points before losing B points, where A and B are integers. Additionally, we find the expected waiting time until one of the two events -- gaining A points or losing B points -- occurs.