商品描述
This book presents a selection of cutting-edge contributions from leading experts in the field, capturing the latest developments in stochastic analysis and its growing interface with neighboring disciplines. Stochastic analysis is a rapidly evolving branch of mathematics focused on the behavior of dynamical systems influenced by randomness. Over the past three decades, it has grown into one of the most vibrant and interdisciplinary areas of research, with profound impact on fields ranging from finance and physics to data science and engineering. Topics include rough path theory, stochastic control, stochastic partial differential equations, random matrices, and applications in machine learning. Building on the success of a recent international conference that brought together researchers from both academia and industry, this proceedings book highlights the depth and breadth of current work in the field. It serves as a valuable resource not only for academic researchers in mathematics, but also for practitioners working in areas such as quantitative finance, data-driven modeling, and applied probability.
商品描述(中文翻譯)
本書呈現了來自該領域領先專家的前沿貢獻，捕捉隨機分析及其與相鄰學科日益增長的交集中的最新發展。隨機分析是一個快速發展的數學分支，專注於受隨機性影響的動態系統行為。在過去的三十年中，它已成為最具活力和跨學科的研究領域之一，對金融、物理、數據科學和工程等領域產生了深遠的影響。
主題包括粗路徑理論、隨機控制、隨機偏微分方程、隨機矩陣以及在機器學習中的應用。
本書基於最近一次國際會議的成功，該會議匯聚了來自學術界和業界的研究人員，突顯了該領域當前工作的深度和廣度。它不僅是數學學術研究者的寶貴資源，也對從事量化金融、數據驅動建模和應用概率等領域的實務工作者具有重要價值。
作者簡介
Dan Crisan is a professor of Mathematics at Imperial College London and Director of the Centre for Doctoral Training in the Mathematics for our Future Climate. He has a Ph.D. in Mathematics from the University of Edinburgh having graduated in December 1996 with a thesis entitled The Problem of Nonlinear Filtering. After his Ph.D. studies, he held a postdoctoral fellowship at Imperial College London and moved to the Statistical Laboratory in Cambridge as an assistant lecturer. Crisan returned to Imperial in 2000, where he was awarded a prestigious Governors' Lectureship. He was promoted to a full professor in 2011. His research is in the wider area of Stochastic Analysis and application. Ilya Chevyrev is currently a researcher at SISSA. Prior to this, he was a Ph.D. student and junior research fellow at the University of Oxford, a postdoc and Mercator Fellow at TU Berlin, and a Reader at the University of Edinburgh. His research focuses on rough analysis. Thomas Cass is Professor of Mathematics at Imperial College London. His research focuses on probability, stochastic analysis, and mathematical data science, with particular emphasis on rough path theory. He completed his PhD at the University of Cambridge and held academic positions at the University of Oxford before joining Imperial in 2011. At Imperial, he directs the EPSRC Centre for Doctoral Training in the Mathematics of Random Systems, a joint initiative with the University of Oxford, and is part of the leadership team for the DataSig I and DataSig II programmes, which develops mathematical tools for analysing complex data. He has been a Visiting Researcher at the Alan Turing Institute and was the Erik Ellentuck Fellow at the Institute for Advanced Study in Princeton. James Foster is currently a lecturer in mathematics at the University of Bath. Previously, he was a Ph.D. student and postdoctoral researcher at the University of Oxford. His research focuses on stochastic numerics, differential equations and their applications to machine learning. Christian Litterer is currently a Lecturer in the Department of Mathematics at the University of York. He completed his PhD and held a postdoctoral position at the University of Oxford. Before joining the University of York, he also held postdoctoral positions at Imperial College London and École Polytechnique. His research interests lie in signatures, rough paths, and their applications in stochastic analysis. Cristopher Salvi is a lecturer in Mathematics and AI at Imperial College London, Department of Mathematics, and Imperial X. Previously, he was a Chapman fellow in Mathematics at Imperial College London and before that he obtained his Ph.D. from the University of Oxford under the supervision of Terry Lyons.
作者簡介(中文翻譯)
丹·克里桑（Dan Crisan）是倫敦帝國學院（Imperial College London）數學教授，並擔任我們未來氣候數學博士培訓中心的主任。他於1996年12月在愛丁堡大學（University of Edinburgh）獲得數學博士學位，論文題目為《非線性濾波問題》（The Problem of Nonlinear Filtering）。在完成博士學位後，他在倫敦帝國學院擔任博士後研究員，隨後轉至劍橋的統計實驗室（Statistical Laboratory）擔任助理講師。克里桑於2000年回到帝國學院，並獲得了著名的董事講座（Governors' Lectureship）。他於2011年晉升為正教授。他的研究領域為隨機分析及其應用。
伊利亞·切維列夫（Ilya Chevyrev）目前是SISSA的研究員。在此之前，他是牛津大學（University of Oxford）的博士生和初級研究員，並曾在柏林工業大學（TU Berlin）擔任博士後和梅卡托爾研究員（Mercator Fellow），以及在愛丁堡大學擔任講師。他的研究重點是粗糙分析。
托馬斯·卡斯（Thomas Cass）是倫敦帝國學院的數學教授。他的研究專注於概率、隨機分析和數學數據科學，特別強調粗糙路徑理論（rough path theory）。他在劍橋大學完成博士學位，並在加入帝國學院之前曾在牛津大學擔任學術職位。於2011年加入帝國學院後，他負責EPSRC隨機系統數學博士培訓中心，這是一個與牛津大學的聯合計劃，並且是DataSig I和DataSig II計劃的領導團隊成員，該計劃開發用於分析複雜數據的數學工具。他曾在艾倫·圖靈研究所（Alan Turing Institute）擔任訪問研究員，並曾是普林斯頓高等研究院（Institute for Advanced Study）埃里克·艾倫塔克研究員（Erik Ellentuck Fellow）。
詹姆斯·福斯特（James Foster）目前是巴斯大學（University of Bath）的數學講師。之前，他是牛津大學的博士生和博士後研究員。他的研究專注於隨機數值分析、微分方程及其在機器學習中的應用。
克里斯蒂安·利特雷（Christian Litterer）目前是約克大學（University of York）數學系的講師。他在牛津大學完成博士學位並擔任博士後職位。在加入約克大學之前，他還曾在倫敦帝國學院和巴黎綜合理工學院（École Polytechnique）擔任博士後職位。他的研究興趣包括簽名、粗糙路徑及其在隨機分析中的應用。
克里斯多福·薩爾維（Cristopher Salvi）是倫敦帝國學院數學系及Imperial X的數學與人工智慧講師。之前，他是倫敦帝國學院的查普曼數學研究員，並在此之前在牛津大學獲得博士學位，指導教授為特里·萊昂斯（Terry Lyons）。
