| 书目名称 | Stochastic Exponential Growth and Lattice Gases |
| 副标题 | Statistical Mechanic |
| 编辑 | Dan Pirjol |
| 视频video | |
| 概述 | Explores a new intersection of statistical mechanics and an area of applied probability.Gives a detailed treatment of the statistical mechanics of certain one-dimensional lattice gas models.Provides M |
| 丛书名称 | SpringerBriefs in Applied Sciences and Technology |
| 图书封面 |  |
| 描述 | .The book discusses a class of discrete time stochastic growth processes for which the growth rate is proportional to the exponential of a Gaussian Markov process. These growth processes appear naturally in problems of mathematical finance as discrete time approximations of stochastic volatility models and stochastic interest rates models such as the Black-Derman-Toy and Black-Karasinski models. These processes can be mapped to interacting one-dimensional lattice gases with long-range interactions. ..The book gives a detailed discussion of these statistical mechanics models, including new results not available in the literature, and their implication for the stochastic growth models. The statistical mechanics analogy is used to understand observed non-analytic dependence of the Lyapunov exponents of the stochastic growth processes considered, which is related to phase transitions in the lattice gas system. The theoretical results are applied to simulations of financial models and are illustrated with Mathematica code. ..The book includes a general introduction to exponential stochastic growth with examples from biology, population dynamics and finance. The presentation does not ass |
| 出版日期 | Book 2022 |
| 关键词 | lattice gases; Black-Derman-Toy model; Black-Karasinski model; Lyapunov exponents; one-dimensional exact |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-031-11143-3 |
| isbn_softcover | 978-3-031-11142-6 |
| isbn_ebook | 978-3-031-11143-3Series ISSN 2191-530X Series E-ISSN 2191-5318 |
| issn_series | 2191-530X |
| copyright | The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 |
发表于 2025-3-21 19:31:19
