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

Abstract:Leading benchmarks for formal theorem proving with large language models are small collections drawn from competition math, such as the IMO and Putnam, that poorly represent field-specific applications. We introduce StochBench, a Lean 4 benchmark of 450 graduate stochastic-processes problems at varying abstraction levels, each paired with its natural-language source. Addressing a field underrepresented in Mathlib, it covers 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. Our Opus 4.8-based agent achieves a 34.9% proof rate (157/450) under a 15-minute per-problem limit. StochBench better represents domain-specific applied mathematics while remaining challenging for advanced provers.

Computation and Language (cs.CL); Logic in Computer Science (cs.LO)

arXiv:2609.09264 [cs.CL]

(or arXiv:2609.09264v1 [cs.CL] for this version)

https://doi.org/10.48550/arXiv.2609.09264 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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