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Inverse Problems for Stochastic Partial Differential Equations (SpringerBriefs on PDEs and Data Science) - Softcover
Synopsis
This book provides a comprehensive and systematic introduction to inverse problems for stochastic partial differential equations (SPDEs), with particular emphasis on stochastic parabolic and hyperbolic equations. It addresses both the unique challenges and new opportunities that arise in the stochastic setting. Key topics include inverse state problems (such as determining unknown initial conditions) and inverse source problems (identifying unknown source terms), with a focus on the mathematical tools essential for their analysis, especially global Carleman estimates tailored to SPDEs. The book explores fundamental issues of uniqueness, stability, and reconstruction under various measurement scenarios, including internal, boundary, and terminal observations. It highlights how stochasticity can fundamentally alter the nature of inverse problems, sometimes enabling solutions where deterministic approaches fail. Reconstruction methods such as Tikhonov regularization are also discussed in detail. This book is intended for graduate students and researchers in applied mathematics, stochastic analysis, and PDEs, as well as practitioners in fields like mathematical finance, physics, and engineering who require rigorous methods for uncertainty quantification. A moderate background in PDEs, functional analysis, and basic stochastic calculus is beneficial.
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About the Author
Qi Lü is a professor at School of Mathematics, Sichuan University, Chengdu, China. He is a sectional speaker at International Congress of Mathematicians (Control Theory and Optimization Section, 2022). He is currently an associate editor/editorial board member of several journals including SIAM Journal on Control and Optimization, ESAIM: Control, Optimisation and Calculus of Variations, Annals of Applied Probability and Systems & Control Letters. His research interests include inverse problems and control theory for deterministic and stochastic partial differential equations and stochastic analysis. Yu Wang is an assistant professor at School of Mathematics, Southwest Jiaotong University, Chengdu, China. His research interests include inverse problems and control theory for stochastic partial differential equations.
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Inverse Problems for Stochastic Partial Differential Equations (Paperback)
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Springer Verlag, Singapore, Singapore, 2026
ISBN 10: 9819590493
ISBN 13: 9789819590490
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Paperback. Condition: new. Paperback. This book provides a comprehensive and systematic introduction to inverse problems for stochastic partial differential equations (SPDEs), with particular emphasis on stochastic parabolic and hyperbolic equations. It addresses both the unique challenges and new opportunities that arise in the stochastic setting. Key topics include inverse state problems (such as determining unknown initial conditions) and inverse source problems (identifying unknown source terms), with a focus on the mathematical tools essential for their analysis, especially global Carleman estimates tailored to SPDEs. The book explores fundamental issues of uniqueness, stability, and reconstruction under various measurement scenarios, including internal, boundary, and terminal observations. It highlights how stochasticity can fundamentally alter the nature of inverse problems, sometimes enabling solutions where deterministic approaches fail. Reconstruction methods such as Tikhonov regularization are also discussed in detail. This book is intended for graduate students and researchers in applied mathematics, stochastic analysis, and PDEs, as well as practitioners in fields like mathematical finance, physics, and engineering who require rigorous methods for uncertainty quantification. A moderate background in PDEs, functional analysis, and basic stochastic calculus is beneficial. This book provides a comprehensive and systematic introduction to inverse problems for stochastic partial differential equations (SPDEs), with particular emphasis on stochastic parabolic and hyperbolic equations. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9789819590490
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Inverse Problems for Stochastic Partial Differential Equations
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Inverse Problems for Stochastic Partial Differential Equations (SpringerBriefs on PDEs and Data Science)
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Inverse Problems for Stochastic Partial Differential Equations
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book provides a comprehensive and systematic introduction to inverse problems for stochastic partial differential equations (SPDEs), with particular emphasis on stochastic parabolic and hyperbolic equations. It addresses both the unique challenges and new opportunities that arise in the stochastic setting. Key topics include inverse state problems (such as determining unknown initial conditions) and inverse source problems (identifying unknown source terms), with a focus on the mathematical tools essential for their analysis, especially global Carleman estimates tailored to SPDEs. The book explores fundamental issues of uniqueness, stability, and reconstruction under various measurement scenarios, including internal, boundary, and terminal observations. It highlights how stochasticity can fundamentally alter the nature of inverse problems, sometimes enabling solutions where deterministic approaches fail. Reconstruction methods such as Tikhonov regularization are also discussed in detail. This book is intended for graduate students and researchers in applied mathematics, stochastic analysis, and PDEs, as well as practitioners in fields like mathematical finance, physics, and engineering who require rigorous methods for uncertainty quantification. A moderate background in PDEs, functional analysis, and basic stochastic calculus is beneficial. Seller Inventory # 9789819590490
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Inverse Problems for Stochastic Partial Differential Equations
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Taschenbuch. Condition: Neu. This item is printed on demand - Print on Demand Titel. Neuware -This book provides a comprehensive and systematic introduction to inverse problems for stochastic partial differential equations (SPDEs), with particular emphasis on stochastic parabolic and hyperbolic equations. It addresses both the unique challenges and new opportunities that arise in the stochastic setting. Key topics include inverse state problems (such as determining unknown initial conditions) and inverse source problems (identifying unknown source terms), with a focus on the mathematical tools essential for their analysis, especially global Carleman estimates tailored to SPDEs. The book explores fundamental issues of uniqueness, stability, and reconstruction under various measurement scenarios, including internal, boundary, and terminal observations. It highlights how stochasticity can fundamentally alter the nature of inverse problems, sometimes enabling solutions where deterministic approaches fail. Reconstruction methods such as Tikhonov regularization are also discussed in detail. This book is intended for graduate students and researchers in applied mathematics, stochastic analysis, and PDEs, as well as practitioners in fields like mathematical finance, physics, and engineering who require rigorous methods for uncertainty quantification. A moderate background in PDEs, functional analysis, and basic stochastic calculus is beneficial.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 148 pp. Englisch. Seller Inventory # 9789819590490
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Inverse Problems for Stochastic Partial Differential Equations
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Taschenbuch. Condition: Neu. Inverse Problems for Stochastic Partial Differential Equations | Qi Lü (u. a.) | Taschenbuch | SpringerBriefs on PDEs and Data Science | viii | Englisch | 2026 | Springer | EAN 9789819590490 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. Seller Inventory # 138068564