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

StochBench：Lean 中针对随机过程的领域特定基准测试

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. 目前用于大语言模型形式化定理证明的主流基准测试，大多是源自国际数学奥林匹克（IMO）和普特南数学竞赛（Putnam）等竞赛数学的小型集合，这些题目难以代表特定领域的实际应用。

We introduce StochBench, a Lean 4 benchmark of 450 graduate stochastic-processes problems at varying abstraction levels, each paired with its natural-language source. 我们推出了 StochBench，这是一个基于 Lean 4 的基准测试，包含 450 道不同抽象程度的研究生水平随机过程题目，每道题都配有其自然语言来源。

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. 针对 Mathlib 中代表性不足的领域，该基准测试涵盖了有限和可数马尔可夫链、更新过程、随机游走、鞅、停时、排队论、布朗运动、随机微积分、弱收敛以及泊松过程和连续时间马尔可夫过程。

Our Opus 4.8-based agent achieves a 34.9% proof rate (157/450) under a 15-minute per-problem limit. 我们基于 Opus 4.8 的智能体在每题 15 分钟的限制下，实现了 34.9%（157/450）的证明成功率。

StochBench better represents domain-specific applied mathematics while remaining challenging for advanced provers. StochBench 更好地代表了领域特定的应用数学，同时对高级证明系统而言仍具有挑战性。