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Titlebook: An Introduction to Continuous-Time Stochastic Processes; Theory, Models, and Vincenzo Capasso,David Bakstein Textbook 2021Latest edition T

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发表于 2025-3-21 16:14:26 | 显示全部楼层 |阅读模式
期刊全称An Introduction to Continuous-Time Stochastic Processes
期刊简称Theory, Models, and
影响因子2023Vincenzo Capasso,David Bakstein
视频video
发行地址Introduces readers to the theory of continuous-time stochastic processes using real-life examples in medicine, finance, and biology.Includes updated exercises, examples, and material based on advances
学科分类Modeling and Simulation in Science, Engineering and Technology
图书封面Titlebook: An Introduction to Continuous-Time Stochastic Processes; Theory, Models, and  Vincenzo Capasso,David Bakstein Textbook 2021Latest edition T
影响因子This textbook, now in its fourth edition, offers a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential equations. Expertly balancing theory and applications, it features concrete examples of modeling real-world problems from biology, medicine, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Unlike other books on stochastic methods that specialize in a specific field of applications, this volume examines the ways in which similar stochastic methods can be applied across different fields..Beginning with the fundamentals of probability, the authors go on to introduce the theory of stochastic processes, the Itô Integral, and stochastic differential equations. The following chapters then explore stability, stationarity, and ergodicity. The second half of the book is dedicated to applications to a variety of fields, including finance, biology, and medicine. Some highlights of this fourth edition include a more rigorous introduction to Gaussian white noise, additional material on the stability of stochastic semigroups used in models of pop
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发表于 2025-3-21 20:33:55 | 显示全部楼层
Stochastic Processeson processes with independent increments, martingales, and Markov processes. The two fundamental classes of processes, Poisson and Wiener, are introduced as well as the larger, more general, class of Lévy processes. Further, a significant introduction to random measures and marked counting processes
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Stability, Stationarity, Ergodicityence. Connections with semigroup representations of Markov dynamical systems on suitable Banach spaces are presented. Ergodic properies and long time behaviour are analyzed, including concepts of stability, invariant distributions and first passage times.
发表于 2025-3-22 12:39:29 | 显示全部楼层
Applications to Finance and Insurancengales and Girsanov’s theorem. It explains the standard Black–Scholes theory and relates it to Kolmogorov’s partial differential equations and the Feynman–Kac formula. Extensions and variations of the standard theory are discussed as well as interest rate models and insurance mathematics.
发表于 2025-3-22 15:04:40 | 显示全部楼层
Applications to Biology and Medicineern research, the fundamentals of self-organizing systems, in particular focusing on the social behavior of multiagent systems, with some applications to economics (“price herding”). It also includes a particular application to the neurosciences, illustrating the importance of stochastic differentia
发表于 2025-3-22 19:25:53 | 显示全部楼层
Textbook 2021Latest editionchastic integrals, and stochastic differential equations. Expertly balancing theory and applications, it features concrete examples of modeling real-world problems from biology, medicine, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Unli
发表于 2025-3-23 01:02:16 | 显示全部楼层
Die Harmonie der Stundenlinien,. As a complement, there is a discussion on environmental noise, in particular evidencing paradoxes that may arise when adding Gaussian white noise to parameters. Models of bounded noise are then discussed. As an example of a multi-scale system with a stochastic geometric structure, a nontrivial model of tumor-driven angiogenesis has been added.
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