A Modern Theory of Random Variation: With Applications in Stochastic Calculus, Financial Mathematics, and Feynman Integration
暫譯: 隨機變異的現代理論：在隨機微積分、金融數學與費曼積分中的應用

Muldowney, Patrick

A Modern Theory of Random Variation: With Applications in Stochastic Calculus, Financial Mathematics, and Feynman Integration
  • 出版商: Wiley
  • 出版日期: 2012-10-30
  • 售價: $4,860
  • 貴賓價: 9.5 折 $4,617
  • 語言: 英文
  • 頁數: 527
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 111816640X
  • ISBN-13: 9781118166406
  • 相關分類: 微積分 Calculus

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商品描述

A ground-breaking and practical treatment of probability and stochastic processes

A Modern Theory of Random Variation is a new and radical re-formulation of the mathematical underpinnings of subjects as diverse as investment, communication engineering, and quantum mechanics. Setting aside the classical theory of probability measure spaces, the book utilizes a mathematically rigorous version of the theory of random variation that bases itself exclusively on finitely additive probability distribution functions.

In place of twentieth century Lebesgue integration and measure theory, the author uses the simpler concept of Riemann sums, and the non-absolute Riemann-type integration of Henstock. Readers are supplied with an accessible approach to standard elements of probability theory such as the central limmit theorem and Brownian motion as well as remarkable, new results on Feynman diagrams and stochastic integrals.

Throughout the book, detailed numerical demonstrations accompany the discussions of abstract mathematical theory, from the simplest elements of the subject to the most complex. In addition, an array of numerical examples and vivid illustrations showcase how the presented methods and applications can be undertaken at various levels of complexity.

A Modern Theory of Random Variation is a suitable book for courses on mathematical analysis, probability theory, and mathematical finance at the upper-undergraduate and graduate levels. The book is also an indispensible resource for researchers and practitioners who are seeking new concepts, techniques and methodologies in data analysis, numerical calculation, and financial asset valuation.

Patrick Muldowney, PhD, served as lecturer at the Magee Business School of the UNiversity of Ulster for over twenty years. Dr. Muldowney has published extensively in his areas of research, including integration theory, financial mathematics, and random variation.

商品描述(中文翻譯)

一部開創性且實用的機率與隨機過程處理

隨機變異的現代理論 是對於投資、通訊工程和量子力學等多樣主題的數學基礎進行全新且激進的重新表述。該書擱置了傳統的機率測度空間理論，採用了一種數學上嚴謹的隨機變異理論，該理論完全基於有限可加的機率分佈函數。

作者使用了比二十世紀的Lebesgue積分和測度理論更簡單的Riemann和，及Henstock的非絕對Riemann型積分。讀者將獲得一種可接近的方式來理解機率理論的標準元素，例如中心極限定理和布朗運動，以及關於Feynman圖和隨機積分的顯著新結果。

在整本書中，詳細的數值示範伴隨著抽象數學理論的討論，從該主題的最簡單元素到最複雜的部分。此外，各種數值範例和生動的插圖展示了所提出的方法和應用如何在不同的複雜程度下進行。

隨機變異的現代理論 是適合於高年級本科生和研究生的數學分析、機率理論和數學金融課程的書籍。該書也是尋求數據分析、數值計算和金融資產評價中新概念、新技術和新方法的研究人員和實務工作者不可或缺的資源。

Patrick Muldowney博士在阿爾斯特大學的Magee商學院擔任講師超過二十年。Muldowney博士在其研究領域，包括積分理論、金融數學和隨機變異方面發表了大量的著作。

作者簡介

PATRICK MULDOWNEY, PhD, served as lecturer in the Magee Business School at the University of Ulster for over twenty years. Dr. Muldowney has published extensively in his areas of research, including integration theory, financial mathematics, and random variation.

作者簡介(中文翻譯)

帕特里克·穆爾道尼（PATRICK MULDOWNEY），博士，在阿爾斯特大學的馬基商學院擔任講師超過二十年。穆爾道尼博士在其研究領域發表了大量的著作，包括整合理論、金融數學和隨機變異。

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