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math.PR2025
Stein's method for models with general clocks: A tutorial
Anton Braverman, Ziv Scully
Diffusion approximations are widely used in the analysis of service systems, providing tractable insights into complex models. While heavy-traffic limit theorems justify these appr…
math.PR2024
Diffusion approximation error for queueing systems with general primitives
Anton Braverman, Ziv Scully
We investigate the steady-state diffusion-approximation error for continuous-time queueing systems with generally distributed primitives. A common picture emerges after analyzing a…
math.PR2023
Steady-state Dirichlet approximation of the Wright-Fisher model using the prelimit generator comparison approach of Stein's method
Anton Braverman, Han L. Gan
The Wright-Fisher model, originating in Wright (1931) is one of the canonical probabilistic models used in mathematical population genetics to study how genetic type frequencies ev…