Probability Theory II: Stochastic Calculus
暫譯: 機率論 II：隨機微積分

Pascucci, Andrea

Probability Theory II: Stochastic Calculus
  • 出版商: Springer
  • 出版日期: 2024-09-03
  • 售價: $2,940
  • 貴賓價: 9.5 折 $2,793
  • 語言: 英文
  • 頁數: 426
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3031631927
  • ISBN-13: 9783031631924
  • 相關分類: 機率統計學 Probability-and-statistics

    • 海外代購書籍(需單獨結帳)

商品描述

This book offers a modern approach to the theory of continuous-time stochastic processes and stochastic calculus. The content is treated rigorously, comprehensively, and independently. In the first part, the theory of Markov processes and martingales is introduced, with a focus on Brownian motion and the Poisson process. Subsequently, the theory of stochastic integration for continuous semimartingales was developed. A substantial portion is dedicated to stochastic differential equations, the main results of solvability and uniqueness in weak and strong sense, linear stochastic equations, and their relation to deterministic partial differential equations. Each chapter is accompanied by numerous examples. This text stems from over twenty years of teaching experience in stochastic processes and calculus within master's degrees in mathematics, quantitative finance, and postgraduate courses in mathematics for applications and mathematical finance at the University of Bologna. The book provides material for at least two semester-long courses in scientific studies (Mathematics, Physics, Engineering, Statistics, Economics, etc.) and aims to provide a solid background for those interested in the development of stochastic calculus theory and its applications. This text completes the journey started with the first volume of Probability Theory I - Random Variables and Distributions, through a selection of advanced classic topics in stochastic analysis.

商品描述(中文翻譯)

這本書提供了一種現代化的方法來探討連續時間隨機過程和隨機微積分的理論。內容經過嚴謹、全面且獨立的處理。在第一部分，介紹了馬可夫過程和鞅的理論，重點放在布朗運動和泊松過程上。隨後，發展了連續半鞅的隨機積分理論。相當大的一部分專門討論隨機微分方程，主要結果包括弱解和強解的可解性和唯一性、線性隨機方程及其與確定性偏微分方程的關係。每一章都附有大量的例子。本書源自於在博洛尼亞大學教授隨機過程和微積分超過二十年的教學經驗，涵蓋數學、量化金融碩士學位及應用數學和數學金融的研究生課程。這本書提供了至少兩個學期的科學研究課程（數學、物理、工程、統計、經濟學等）的教材，旨在為有興趣於隨機微積分理論及其應用發展的人士提供堅實的基礎。本書完成了與《概率論 I - 隨機變數與分佈》第一卷開始的旅程，通過選擇隨機分析中的一些高級經典主題。

作者簡介

Andrea Pascucci is a professor of Probability and Mathematical Statistics at the Alma Mater Studiorum - University of Bologna. His research activity encompasses various aspects of the theory of stochastic differential equations for diffusions and jump processes, degenerate partial differential equations, and their applications to mathematical finance. He has authored 6 books and over 80 scientific articles on the following topics: linear and nonlinear Kolmogorov-Fokker-Planck equations; regularity and asymptotic estimates of transition densities for multidimensional diffusions and jump processes; free boundary problems, optimal stopping, and applications to American-style financial derivatives; Asian options and volatility models. He has been invited as a speaker at more than 40 international conferences. He serves as an editor for the Journal of Computational Finance and is the director of a postgraduate program in Mathematical Finance at the University of Bologna.

作者簡介(中文翻譯)

安德烈亞·帕斯庫奇是博洛尼亞大學（Alma Mater Studiorum - University of Bologna）概率與數學統計的教授。他的研究活動涵蓋隨機微分方程的理論，包括擴散和跳躍過程、退化偏微分方程及其在數學金融中的應用。他已出版6本書籍和80多篇科學文章，主題包括：線性和非線性科爾莫哥洛夫-福克-普朗克方程；多維擴散和跳躍過程的轉移密度的正則性和漸近估計；自由邊界問題、最佳停止及其在美式金融衍生品中的應用；亞洲期權和波動率模型。他曾受邀在40多個國際會議上擔任演講者。並擔任《計算金融期刊》（Journal of Computational Finance）的編輯，以及博洛尼亞大學數學金融研究所的研究生課程主任。

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