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Titlebook: Stochastic Calculus; An Introduction Thro Paolo Baldi Textbook 2017 Springer International Publishing AG 2017 stochastic calculus.stochasti

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发表于 2025-3-21 19:42:07 | 显示全部楼层 |阅读模式
书目名称Stochastic Calculus
副标题An Introduction Thro
编辑Paolo Baldi
视频videohttp://file.papertrans.cn/878/877866/877866.mp4
概述Provides a self-contained introduction to stochastic calculus.Includes applications and numerical methods.Features more than 200 exercises with detailed solutions
丛书名称Universitext
图书封面Titlebook: Stochastic Calculus; An Introduction Thro Paolo Baldi Textbook 2017 Springer International Publishing AG 2017 stochastic calculus.stochasti
描述.This book provides a comprehensive introduction to the theory of stochastic calculus and some of its applications. It is the only textbook on the subject to include more than two hundred exercises with complete solutions..After explaining the basic elements of probability, the author introduces more advanced topics such as Brownian motion, martingales and Markov processes. The core of the book covers stochastic calculus, including stochastic differential equations, the relationship to partial differential equations, numerical methods and simulation, as well as applications of stochastic processes to finance. The final chapter provides detailed solutions to all exercises, in some cases presenting various solution techniques together with a discussion of advantages and drawbacks of the methods used.. .Stochastic Calculus .will be particularly useful to advanced undergraduate and graduate students wishing to acquire a solid understanding of the subject through the theory and exercises. Including full mathematical statements and rigorous proofs, this book is completely self-contained and suitable for lecture courses as well as self-study..
出版日期Textbook 2017
关键词stochastic calculus; stochastic calculus exercises; probability elements; stochastic processes; Brownian
版次1
doihttps://doi.org/10.1007/978-3-319-62226-2
isbn_softcover978-3-319-62225-5
isbn_ebook978-3-319-62226-2Series ISSN 0172-5939 Series E-ISSN 2191-6675
issn_series 0172-5939
copyrightSpringer International Publishing AG 2017
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Stochastic Differential Equations,t. 9.8 we obtain some .. estimates that will allow us to specify the regularity of the paths and the dependence from the initial conditions. In the last sections we shall see that the solution of a stochastic differential equation is a Markov process and even a diffusion associated to a differential
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PDE Problems and Diffusions,are very useful from two points of view. First of all, for the investigation and a better understanding of the properties of the solutions of these PDEs. Moreover, in some situations, they allow to compute the solution of the PDE (through the explicit computation of the expectation of the correspond
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,∗Simulation,ula in order to do this and one must recourse to approximations and numerical methods. We have seen in the previous chapter that sometimes such an expectation can be obtained by solving a PDE problem so that specific numerical methods for PDEs, such as finite elements, can be employed. Simulation of
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PDE Problems and Diffusions,Es. Moreover, in some situations, they allow to compute the solution of the PDE (through the explicit computation of the expectation of the corresponding functional) or the expectation of the functional (by solving the PDE explicitly). The exercises of this chapter and Exercise 12.8 provide some instances of this way of reasoning.
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,∗Simulation,ectation can be obtained by solving a PDE problem so that specific numerical methods for PDEs, such as finite elements, can be employed. Simulation of diffusion processes is another option which is explored in this chapter.
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