| 书目名称 | Continuous Parameter Markov Processes and Stochastic Differential Equations |
| 编辑 | Rabi Bhattacharya,Edward C. Waymire |
| 视频video | |
| 概述 | Builds from simple examples to formal proofs, illuminating key ideas and computations.Markov processes has an elegant and profound mathematical theory and a great diversity of applications.Set of cour |
| 丛书名称 | Graduate Texts in Mathematics |
| 图书封面 |  |
| 描述 | .This graduate text presents the elegant and profound theory of continuous parameter Markov processes and many of its applications. The authors focus on developing context and intuition before formalizing the theory of each topic, illustrated with examples..After a review of some background material, the reader is introduced to semigroup theory, including the Hille–Yosida Theorem, used to construct continuous parameter Markov processes. Illustrated with examples, it is a cornerstone of Feller’s seminal theory of the most general one-dimensional diffusions studied in a later chapter. This is followed by two chapters with probabilistic constructions of jump Markov processes, and processes with independent increments, or Lévy processes. The greater part of the book is devoted to Itô’s fascinating theory of stochastic differential equations, and to the study of asymptotic properties of diffusions in all dimensions, such as explosion, transience, recurrence, existence of steady states, and the speed of convergence to equilibrium. A broadly applicable functional central limit theorem for ergodic Markov processes is presented with important examples. Intimate connections be |
| 出版日期 | Textbook 2023 |
| 关键词 | Hille-Yoshida theorem; Lévy processes; Markov processes with jumps; Markov property; central limit theor |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-031-33296-8 |
| isbn_softcover | 978-3-031-34153-3 |
| isbn_ebook | 978-3-031-33296-8Series ISSN 0072-5285 Series E-ISSN 2197-5612 |
| issn_series | 0072-5285 |
| copyright | Springer Nature Switzerland AG 2023 |
发表于 2025-3-21 16:47:04
