arXiv Computation and Language By Idan Davidovich, Debargha Ganguly, Vikash Singh, Vipin Chaudhary

StochBench: A Domain-Specific Benchmark for Stochastic Processes in Lean

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StochBench is a new Lean 4 benchmark comprising 450 graduate‑level stochastic‑process problems, each linked to its natural‑language source. It covers a wide range of topics—finite and countable Markov chains, renewal processes, random walks, martingales, stopping times, queues, Brownian motion, stochastic calculus, weak convergence, and Poisson and continuous‑time Markov processes—addressing a field underrepresented in Mathlib. An Opus 4.8‑based agent achieved a 34.9% proof rate (157/450) within a 15‑minute per‑problem limit, demonstrating the benchmark’s difficulty for advanced provers.

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