Stochastic Partial Differential Equations with Additive Gaussian Noise

加性高斯噪声随机偏微分方程:分析和推理

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作      者
出  版 社
出版时间
2022年10月12日
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ISBN
9789811264450
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页      码
200 pp
语      种
英文
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图书简介
The stochastic partial differential equations (SPDEs) arise in many applications of the probability theory. This monograph will focus on two particular (and probably the most known) equations: the stochastic heat equation and the stochastic wave equation.The focus is on the relationship between the solutions to the SPDEs and the fractional Brownian motion (and related processes). An important point of the analysis is the study of the asymptotic behavior of the p-variations of the solutions to the heat or wave equations driven by space-time Gaussian noise or by a Gaussian noise with a non-trivial correlation in space.The book is addressed to public with a reasonable background in probability theory. The idea is to keep it self-contained and avoid using of complex techniques. We also chose to insist on the basic properties of the random noise and to detail the construction of the Wiener integration with respect to them. The intention is to present the proofs complete and detailed.Key FeaturesThe book is self-contained and it is accessible to graduate and undergraduate students and even to professionalsIt contains a quasi-complete description of some multiparameter Gaussian processesSeveral aspects in this book have not been treated before in any monograph: the full description of the relationships between solution to SPDEs and fractional processes, the limit behavior of the p-variation for the solutions to stochastic heat and wave equations, the statistical inference for SPDEs
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