StochBench: A Domain-Specific Benchmark for Stochastic Processes in Lean
StochBench introduces 450 graduate-level stochastic-processes problems in Lean 4; an Opus 4.8-based agent proved 34.9% under a 15-minute limit.
StochBench is a Lean 4 benchmark of 450 graduate stochastic-processes problems, each paired with its natural-language source, covering Markov chains, renewal processes, martingales, Brownian motion, stochastic calculus, weak convergence, and Poisson and continuous-time Markov processes. The benchmark addresses field-specific applied mathematics underrepresented in Mathlib, unlike competition-math-dominated suites such as IMO and Putnam collections. An Opus 4.8-based agent achieved a 34.9% proof rate (157/450) under a 15-minute per-problem limit, showing the benchmark remains challenging for advanced provers.