StochBench: A Domain-Specific Benchmark for Stochastic Processes in Lean
Idan Davidovich, Debargha Ganguly, Vikash Singh, Vipin Chaudhary
Case Western Reserve University
Published September 8, 2026 · on the feed September 10, 2026 · ▲ 8 · arXiv 2609.09264
The 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.
The Brief
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Transcript
StochBench. A Domain-Specific Benchmark for Stochastic Processes in Lean. By Idan Davidovich and three others, from Case Western Reserve University. Published on the eighth of September. No code repository is linked to it, though it does publish its weights.
The leading benchmarks for formal theorem proving with language models are small collections drawn from competition mathematics, the IMO and Putnam among them. The authors argue they poorly represent how proofs are needed in particular fields of application. Stochastic processes are one such field, and it is a field underrepresented in Mathlib.
StochBench measures whether a prover can formally prove graduate-level results about stochastic processes in Lean 4. Problems come at varying levels of abstraction, and each is paired with its natural-language source, so the formal statement can be read against the original.
There are four hundred and fifty problems. They cover 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.
The authors' own agent, based on Opus 4.8, achieves a proof rate of thirty-four point nine percent, one hundred and fifty-seven problems out of four hundred and fifty, with a limit of fifteen minutes per problem.
StochBench is offered as a better picture of applied mathematics in a specific domain, and one that still resists advanced provers. Its contrast with competition sets is the point. Instead of a small collection of contest problems, it offers hundreds of problems from one graduate field, spread across every one of those topics, with a proof rate that leaves most of them still unproved by the authors' own agent.
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Chapter 1 🧩 · The problem
Provers ace contest maths. Can they help in a real field? Start with the gap.
You want to know whether language-model provers can help with real mathematics in Lean. The leading benchmarks are small sets of competition problems, from contests like the IMO and Putnam.
The road ahead
- 1 · The problem ~7 min Competition benchmarks give provers one aggregate score, which says little about how they handle the recurring arguments of a real field like stochastic processes.
- 2 · What came before ~3 min
- 3 · The key idea ~9 min StochBench tests provers deeply on one field, graduate stochastic processes, with each Lean statement paired with its source and strict rules for what counts.
- 4 · Choose your own research ~3 min
- 5 · How it works ~3 min
- 6 · The experiment ~6 min You’ll guess: Given a time limit per problem, what share of the graduate stochastic-processes problems did the authors' Opus-based proof agent prove?
- 7 · The viva ~5 min Three questions from the examiners, answered in your own words. Win it for the paper’s trophy.
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