2014/08/23 by Muruhan Rathinam, Rathinam, Muruhan
Business, Management and Accounting · Mathematics · #Advanced Queuing Theory Analysis #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Numerical Analysis (math.NA) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1408.5527
openalex publication_date 2014/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Tau leap schemes were originally designed for the efficient time stepping of\ndiscrete state and continuous in time Markov processes arising in stochastic\nchemical kinetics. Previous convergence results on tau leaping schemes have\nbeen restricted to systems that remain in a bounded subdomain (which may depend\non the initial condition) or satisfy global Lipschitz conditions on\npropensities. This paper extends the convergence results to fairly general tau\nleap schemes applied to unbounded systems that possess certain moment growth\nbounds. Specifically, we prove a weak convergence result, which shows order q\nconvergence of all moments under certain form of moment growth bound\nassumptions on the stochastic chemical system and the tau leap method, as well\nas polynomial bound assumption on the propensity functions. The results are\nstated for a general class of Markov processes with integN as their state\nspace.\n