Datasets:
Tasks:
Text Generation
Languages:
English
Size:
1K - 10K
ArXiv:
Tags:
Formal theorem proving
Lean 4
Stochastic processes
Mathematical reasoning
Natural language processing
Autoformalization
License:
Add link to paper
#2
by nielsr HF Staff - opened
README.md
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---
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license: cc-by-nc-sa-4.0
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task_categories:
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- text-generation
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-
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- en
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tags:
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- Formal theorem proving
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- Lean 4
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- Mathematical reasoning
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- Natural language processing
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- Autoformalization
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pretty_name: StochBench
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size_categories:
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- n<1K
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---
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# StochBench
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StochBench is a Lean 4 benchmark of **450 graduate stochastic-process problems**, each paired with its natural-language statement. It evaluates proof agents on graduate stochastic processes. Topics include finite and countable Markov chains, martingales, stopping times, renewal processes, random walks, queues, Brownian motion, stochastic calculus, Poisson processes, and weak convergence.
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The benchmark contains direct and abstracted formalizations, with explicit assumptions for each target. The informal-formal pairs can be used for autoformalization training, and checked proofs can provide supervision for proof generation. Shared definitions support further formalization in Lean.
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{
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"question_id": 8,
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"problem_name": "stochastic_processes_martingale_1",
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"informal_statement": "Consider biased gambler’s ruin: at each step, the gambler gains one dollar
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"topic": "Martingales & stopping"
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}
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```
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---
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language:
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- en
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license: cc-by-nc-sa-4.0
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size_categories:
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- n<1K
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task_categories:
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- text-generation
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pretty_name: StochBench
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tags:
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- Formal theorem proving
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- Lean 4
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- Mathematical reasoning
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- Natural language processing
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- Autoformalization
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---
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# StochBench
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**Paper:** [StochBench: A Domain-Specific Benchmark for Stochastic Processes in Lean](https://huggingface.co/papers/2609.09264)
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StochBench is a Lean 4 benchmark of **450 graduate stochastic-process problems**, each paired with its natural-language statement. It evaluates proof agents on graduate stochastic processes. Topics include finite and countable Markov chains, martingales, stopping times, renewal processes, random walks, queues, Brownian motion, stochastic calculus, Poisson processes, and weak convergence.
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The benchmark contains direct and abstracted formalizations, with explicit assumptions for each target. The informal-formal pairs can be used for autoformalization training, and checked proofs can provide supervision for proof generation. Shared definitions support further formalization in Lean.
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{
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"question_id": 8,
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"problem_name": "stochastic_processes_martingale_1",
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"informal_statement": "Consider biased gambler’s ruin: at each step, the gambler gains one dollar
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with probability p and losses one dollar with probability (1 − p).
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Let X_n be the money in purse at time n.
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Show that if p = 1/2, then (X_n) is a martingale.",
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"topic": "Martingales & stopping"
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}
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```
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