Waiting times for patterns in Markov chains

• Grant number: 25/06174-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2025
• End date: June 30, 2026
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Renato Jacob Gava
• Grantee: Eduardo Rio Oliveira
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated research grant: 23/13453-5 - Stochastic systems modeling, AP.TEM

Abstract

Consider a sequence of Markov dependent trials where each trial pro-duces a letter of a nite alphabet. Given a collection of patterns, we lookat this sequence till the moment at which one of these patterns appears asa run. We show how the method of gambling teams may be employed to tond mean waiting time of the collection, its probability generating functionand compute the probability that a given pattern is the rst one to occur.First we deal with a two-state Markov chain by one technique, then we facethe problem for a multistate Markov chain by another technique.