BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Theodore Grunberg DTSTART:20250508T150000Z DTEND:20250508T153000Z DTSTAMP:20260421T124113Z UID:MoRN/122 DESCRIPTION:Title: E rror bounds for the linear noise approximation to stationary distributions of chemical reaction networks\nby Theodore Grunberg as part of Semina r on the Mathematics of Reaction Networks\n\n\nAbstract\nSpecies interacti ng according to chemical reactions are often modeled by a continuous time Markov chain that describes the evolution of counts of the species over ti me. Such Markov chains typically have a large or infinite number of states and are thus computationally difficult to analyze. Therefore\, approximat ions exploiting the fact that the volume and molecular counts are both lar ge are often used. The most common such approximations are the reaction ra te equations (RREs)\, which are a deterministic model\, and the linear noi se approximation (LNA)\, which is a diffusion approximation to fluctuation s about the solution of the RREs. Limit theorem results\, due to Kurtz (19 71)\, establish the validity of the RREs and of the LNA for finite times. However\, such results do not justify approximating the stationary distrib ution of a chemical reaction network using the RREs or LNA. The validity o f these approximations for the stationary distribution has only been inves tigated for special cases\, such as when the Markov chain’s state space is bounded in concentration\, or when the chemical reaction network has a special structure. Here\, we use Stein’s method to derive bounds on the approximation error for the LNA applied to the stationary distribution of a chemical reaction network. Specifically\, we give a non-asymptotic bound on the 1-Wasserstein distance between an appropriately scaled Markov chai n and its LNA\, under certain technical conditions\, that decays to zero w ith increasing system size. Our results do not require that the Markov ch ain’s state space be bounded\, nor do they require that the chemical rea ction network have a special structure. We further show how global stabili ty properties of an equilibrium point of the RREs are sufficient to obtain such error bounds. Our results can be used to check when the LNA is a sui table approximation of the stationary distribution of a chemical reaction network without having to perform computationally costly simulations.\n LOCATION:https://researchseminars.org/talk/MoRN/122/ END:VEVENT END:VCALENDAR