Collaborative Proposal: Strong Stochastic Simulation of Stochastic Processes Theory and Applications

合作提案：随机过程理论与应用的强随机模拟

• 批准号: 1720451
• 负责人: Jose Blanchet
• 金额: $ 20.09万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-09-01 至 2018-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1720451&HistoricalAwards=false
• 关键词: Collaborative; Proposal; Strong; Stochastic; Simulation

High performance computing of continuous random structures arises in a large body of scientific and engineering investigations. For example, these structures are used in environmental models for floods in different geographical areas, which are subject to random measurement errors. They are also used in the prediction and mitigation planning of potential disasters. However, these random structures are impossible to capture in a computer without incurring bias, due to their continuous nature. This research project investigates a new framework for the numerical analysis of continuous random structures. It achieves stronger error control, compared to current state-of-the-art methods, at basically the same computational cost. If successful, the framework and algorithms to be investigated will facilitate analysis and performance evaluation of fundamental random structures of interests to a broad community of scientists and engineers. To enhance the broader impact, the Principal Investigators will train graduate students through research and integrate the results from this research into new graduate courses in scientific computing. This project investigates a new Monte Carlo framework for continuous stochastic structures (such as differential equations and random fields). The main innovative feature of the framework is the ability to approximate a continuous random object by a fully simulatable (typically piece-wise constant) object with a uniform error bound in the path space with 100% certainty. The error bound is user-specified and can be sequentially refined. Research projects involve developing simulation algorithms for fundamental random structures of interests. These include: Gaussian random fields, Levy processes, fractional Brownian motion, max-stable fields, etc. The algorithms are scalable in the sense of being easily extendable to more complex models by applying the continuous mapping principle with quantifiable error analysis. An important aspect of the methodology is the connection established between Monte Carlo simulation and the theory of rough paths in the setting of stochastic analysis.

连续随机结构的高性能计算出现在大量的科学和工程研究中。例如，这些结构用于不同地理区域洪水的环境模型，这些模型会受到随机测量误差的影响。它们还用于潜在灾害的预测和减灾规划。然而，由于它们的连续性，这些随机结构不可能在不产生偏差的情况下在计算机中捕获。该研究项目研究了连续随机结构数值分析的新框架。与当前最先进的方法相比，它以基本相同的计算成本实现了更强的错误控制。如果成功，要研究的框架和算法将有助于对广大科学家和工程师感兴趣的基本随机结构进行分析和性能评估。为了扩大更广泛的影响，首席研究员将通过研究来培训研究生，并将这项研究的结果整合到新的科学计算研究生课程中。该项目研究了连续随机结构（例如微分方程和随机场）的新蒙特卡罗框架。该框架的主要创新特征是能够通过完全可模拟（通常是分段常数）对象来近似连续随机对象，并且在路径空间中具有统一的误差界限，并且具有 100% 的确定性。误差范围是用户指定的并且可以按顺序进行细化。研究项目涉及开发感兴趣的基本随机结构的模拟算法。这些包括：高斯随机场、Levy 过程、分数布朗运动、最大稳定场等。通过应用连续映射原理和可量化误差分析，这些算法可以轻松扩展到更复杂的模型，从这个意义上说，这些算法是可扩展的。该方法的一个重要方面是蒙特卡罗模拟与随机分析背景下的粗糙路径理论之间建立的联系。

项目成果

Perfect sampling of GI/GI/c queues

GI/GI/c 队列的完美采样

• DOI: 10.1007/s11134-018-9573-2
• 发表时间: 2018-03
• 期刊: Queueing Systems
• 影响因子: 1.2
• 作者: Blanchet, Jose;Dong, Jing;Pei, Yanan
• 通讯作者: Pei, Yanan

Exact sampling of the infinite horizon maximum of a random walk over a nonlinear boundary

非线性边界上随机游走的无限水平最大值的精确采样

• DOI: 10.1017/jpr.2019.9
• 发表时间: 2019-03
• 期刊: Journal of Applied Probability
• 影响因子: 1
• 作者: Blanchet, Jose;Dong, Jing;Liu, Zhipeng
• 通讯作者: Liu, Zhipeng

Exact sampling for some multi-dimensional queueing models with renewal input

具有更新输入的某些多维排队模型的精确采样

• DOI: 10.1017/apr.2019.45
• 发表时间: 2019-12
• 期刊: Advances in Applied Probability
• 影响因子: 1.2
• 作者: Blanchet, Jose;Pei, Yanan;Sigman, Karl
• 通讯作者: Sigman, Karl