2010/03/12 by Stephen R. Chestnut, Stephen Chestnut, Chestnut, Stephen +3
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #37A25 #37A30 #37M25 #60C05 #60J10 #60J22 #65C40 #Complex Network Analysis Techniques #Discrete Mathematics (cs.DM) #FOS: Biological sciences #FOS: Computer and information sciences #FOS: Mathematics #Genomics (q-bio.GN) #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #cs.DM #math.PR #msc:37A25 #msc:37A30 #msc:37M25 #msc:60C05 #msc:60J10 #msc:60J22 #msc:65C40 #q-bio.GN
paper · pdf · doi:10.48550/arxiv.1003.2649
12 pages, 2 tables
arxiv created 2010/03/12 · openalex publication_date 2010/03/12 · arxiv updated 2010/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We apply Doeblin's ergodicity coefficient as a computational tool to approximate the occupancy distribution of a set of states in a homogeneous but possibly non-stationary finite Markov chain. Our approximation is based on new properties satisfied by this coefficient, which allow us to approximate a chain of duration n by independent and short-lived realizations of an auxiliary homogeneous Markov chain of duration of order ln(n). Our approximation may be particularly useful when exact calculations via first-step methods or transfer matrices are impractical, and asymptotic approximations may not be yet reliable. Our findings may find applications to pattern problems in Markovian and non-Markovian sequences that are treatable via embedding techniques.