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发生在大量的科学和工程研究中。例如，这些结构用于在不同地理区域的洪水环境模型中，这些洪水会遇到随机测量错误。它们还用于潜在灾难的预测和缓解计划。但是，由于它们的持续性，这些随机结构在没有产生偏见的情况下就无法在计算机中捕获。该研究项目研究了一个新的框架，用于连续随机结构的数值分析。与当前的最新方法相比，它以相同的计算成本来实现更强的误差控制。如果成功，将要研究的框架和算法将促进对广泛的科学家和工程师社区的基本随机结构的分析和绩效评估。为了增强更广泛的影响，首席研究人员将通过研究培训研究生，并将这项研究的结果整合到科学计算的新研究生课程中。该项目研究了一个新的蒙特卡洛框架，用于连续的随机结构（例如微分方程和随机场）。该框架的主要创新特征是能够通过完全模拟（通常是零件的常数）对象近似连续的随机对象，该对象具有100％确定性的路径空间中均匀误差。绑定的错误是用户指定的，并且可以顺序完善。研究项目涉及为利益基本随机结构开发模拟算法。其中包括：高斯随机字段，征费过程，分数布朗运动，最大稳定场等。通过应用可量化的误差分析，将连续映射原理应用于更复杂的模型，从而易于扩展到更复杂的模型。该方法的一个重要方面是在随机分析的环境中蒙特卡洛模拟与粗糙路径理论之间建立的联系。

项目成果

Perfect sampling of GI/GI/c queues

• DOI: 10.1007/s11134-018-9573-2
• 发表时间: 2015-08
• 期刊: Queueing Systems
• 影响因子: 1.2
• 作者: J. Blanchet;Jing Dong;Yanan Pei

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
• 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

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
• 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