Introduction to Stochastic Partial Differential Equations
Seiten
2017
|
1st ed. 2017
Springer Berlin (Verlag)
978-3-642-16535-1 (ISBN)
Springer Berlin (Verlag)
978-3-642-16535-1 (ISBN)
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This book presents the theory of parabolic SPDEs. It considers SPDEs driven by random measures and discontinuous semimartingales and includes the theory of SPDEs driven by Levy processes as special cases.
The $L_2$-theory of parabolic SPDEs is presented in this book. The development of the theory of SPDEs is motivated by problems arising in practice surrounding the numerical calculations of nonlinear filters for partially observed diffusion processes. To address these questions, the dependence of SPDEs on the driving semimartingales is investigated and new results on their numerical approximations are also given. In contrast to previous expositions, SPDEs driven by random measures and discontinuous semimartingales are also considered, and the theory of SPDEs driven by Levy processes are included as special cases. The author introduces a more general theory of SPDEs developing the theory of stochastic evolution equations in Banach spaces. He presents applications to large classes of linear and nonlinear SPDEs and , in particular, he developes a theory of SPDEs with unbounded coefficients in weighted Sobolev spaces. In this unique book regularity properties of the solutions are obtained via new results on dependence of the solutions on parameters, and existence and uniqueness theorems for parabolic SPDEs on smooth domains of $R^d$ are proven. Furthermore, the present book makes the theory more accessible for beginners, because initial linear parabolic SPDEs on the whole $R^d$ are considered, and the main existence and uniqueness results are obtained by elementary methods while exercises and applications are also provided
The $L_2$-theory of parabolic SPDEs is presented in this book. The development of the theory of SPDEs is motivated by problems arising in practice surrounding the numerical calculations of nonlinear filters for partially observed diffusion processes. To address these questions, the dependence of SPDEs on the driving semimartingales is investigated and new results on their numerical approximations are also given. In contrast to previous expositions, SPDEs driven by random measures and discontinuous semimartingales are also considered, and the theory of SPDEs driven by Levy processes are included as special cases. The author introduces a more general theory of SPDEs developing the theory of stochastic evolution equations in Banach spaces. He presents applications to large classes of linear and nonlinear SPDEs and , in particular, he developes a theory of SPDEs with unbounded coefficients in weighted Sobolev spaces. In this unique book regularity properties of the solutions are obtained via new results on dependence of the solutions on parameters, and existence and uniqueness theorems for parabolic SPDEs on smooth domains of $R^d$ are proven. Furthermore, the present book makes the theory more accessible for beginners, because initial linear parabolic SPDEs on the whole $R^d$ are considered, and the main existence and uniqueness results are obtained by elementary methods while exercises and applications are also provided
| Reihe/Serie | Stochastic Modelling and Applied Probability ; 65 |
|---|---|
| Zusatzinfo | X, 340 p. |
| Verlagsort | Berlin |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik |
| Schlagworte | 60H15, 35R60 • Ito´s Formula in Banach Spaces • nonlinear filtering • Stochastic Evolution Equations • Stochastic PDEs |
| ISBN-10 | 3-642-16535-4 / 3642165354 |
| ISBN-13 | 978-3-642-16535-1 / 9783642165351 |
| Zustand | Neuware |
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