# Stochastic Partial Differential Equations With L Vy Noise

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This work considers a small random perturbation of alpha-stable jump type nonlinear reaction-diffusion equations with Dirichlet boundary conditions over an interval. It has two stable points whose domains of attraction meet in a separating manifold with several saddle points. Extending a method developed by Imkeller and Pavlyukevich it proves that in contrast to a Gaussian perturbation, the expected exit and transition times between the domains of attraction depend polynomially on the noise intensity in the small intensity limit. Moreover the solution exhibits metastable behavior: there is a polynomial time scale along which the solution dynamics correspond asymptotically to the dynamic behavior of a finite-state Markov chain switching between the stable states.

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## Product Details :

**Genre** |
: Mathematics |

**Author** |
: Arnaud Debussche |

**Publisher** |
: Springer |

**Release** |
: 2013-10-01 |

**Total Pages** |
: 165 Pages |

**ISBN** |
: 9783319008288 |

Comprehensive monograph by two leading international experts; includes applications to statistical and fluid mechanics and to finance.

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## Product Details :

**Genre** |
: Mathematics |

**Author** |
: S. Peszat |

**Publisher** |
: Cambridge University Press |

**Release** |
: 2007-10-11 |

**Total Pages** |
: 432 Pages |

**ISBN** |
: 9780521879897 |

The study of graph structure has advanced in recent years with great strides: finite graphs can be described algebraically, enabling them to be constructed out of more basic elements. Separately the properties of graphs can be studied in a logical language called monadic second-order logic. In this book, these two features of graph structure are brought together for the first time in a presentation that unifies and synthesizes research over the last 25 years. The authors not only provide a thorough description of the theory, but also detail its applications, on the one hand to the construction of graph algorithms, and, on the other to the extension of formal language theory to finite graphs. Consequently the book will be of interest to graduate students and researchers in graph theory, finite model theory, formal language theory, and complexity theory.

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## Product Details :

**Genre** |
: Mathematics |

**Author** |
: Bruno Courcelle |

**Publisher** |
: Cambridge University Press |

**Release** |
: 2012-06-14 |

**Total Pages** |
: 743 Pages |

**ISBN** |
: 9780521898331 |

The sphere is what might be called a perfect shape. Unfortunately nature is imperfect and many bodies are better represented by an ellipsoid. The theory of ellipsoidal harmonics, originated in the nineteenth century, could only be seriously applied with the kind of computational power available in recent years. This, therefore, is the first book devoted to ellipsoidal harmonics. Topics are drawn from geometry, physics, biosciences and inverse problems. It contains classical results as well as new material, including ellipsoidal bi-harmonic functions, the theory of images in ellipsoidal geometry and vector surface ellipsoidal harmonics, which exhibit an interesting analytical structure. Extended appendices provide everything one needs to solve formally boundary value problems. End-of-chapter problems complement the theory and test the reader's understanding. The book serves as a comprehensive reference for applied mathematicians, physicists, engineers and for anyone who needs to know the current state of the art in this fascinating subject.

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## Product Details :

**Genre** |
: Mathematics |

**Author** |
: George Dassios |

**Publisher** |
: Cambridge University Press |

**Release** |
: 2012-07-12 |

**Total Pages** |
: Pages |

**ISBN** |
: 9781139510134 |

As a relatively new area in mathematics, stochastic partial differential equations (PDEs) are still at a tender age and have not yet received much attention in the mathematical community. Filling the void of an introductory text in the field, Stochastic Partial Differential Equations introduces PDEs to students familiar with basic probability theor

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## Product Details :

**Genre** |
: Mathematics |

**Author** |
: Pao-Liu Chow |

**Publisher** |
: CRC Press |

**Release** |
: 2007-03-19 |

**Total Pages** |
: 281 Pages |

**ISBN** |
: 9781000738216 |

This major revision of Berstel and Perrin's classic Theory of Codes has been rewritten with a more modern focus and a much broader coverage of the subject. The concept of unambiguous automata, which is intimately linked with that of codes, now plays a significant role throughout the book, reflecting developments of the last 20 years. This is complemented by a discussion of the connection between codes and automata, and new material from the field of symbolic dynamics. The authors have also explored links with more practical applications, including data compression and cryptography. The treatment remains self-contained: there is background material on discrete mathematics, algebra and theoretical computer science. The wealth of exercises and examples make it ideal for self-study or courses. In summary, this is a comprehensive reference on the theory of variable-length codes and their relation to automata.

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## Product Details :

**Genre** |
: Mathematics |

**Author** |
: Jean Berstel |

**Publisher** |
: Cambridge University Press |

**Release** |
: 2010 |

**Total Pages** |
: 634 Pages |

**ISBN** |
: 9780521888318 |

This Festschrift contains five research surveys and thirty-four shorter contributions by participants of the conference ''Stochastic Partial Differential Equations and Related Fields'' hosted by the Faculty of Mathematics at Bielefeld University, October 10–14, 2016. The conference, attended by more than 140 participants, including PostDocs and PhD students, was held both to honor Michael Röckner's contributions to the field on the occasion of his 60th birthday and to bring together leading scientists and young researchers to present the current state of the art and promising future developments. Each article introduces a well-described field related to Stochastic Partial Differential Equations and Stochastic Analysis in general. In particular, the longer surveys focus on Dirichlet forms and Potential theory, the analysis of Kolmogorov operators, Fokker–Planck equations in Hilbert spaces, the theory of variational solutions to stochastic partial differential equations, singular stochastic partial differential equations and their applications in mathematical physics, as well as on the theory of regularity structures and paracontrolled distributions. The numerous research surveys make the volume especially useful for graduate students and researchers who wish to start work in the above-mentioned areas, or who want to be informed about the current state of the art.

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## Product Details :

**Genre** |
: Mathematics |

**Author** |
: Andreas Eberle |

**Publisher** |
: Springer |

**Release** |
: 2018-07-03 |

**Total Pages** |
: 574 Pages |

**ISBN** |
: 9783319749297 |

The first edition of Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach, gave a comprehensive introduction to SPDEs. In this, the second edition, the authors build on the theory of SPDEs driven by space-time Brownian motion, or more generally, space-time Lévy process noise. Applications of the theory are emphasized throughout. The stochastic pressure equation for fluid flow in porous media is treated, as are applications to finance. Graduate students in pure and applied mathematics as well as researchers in SPDEs, physics, and engineering will find this introduction indispensible. Useful exercises are collected at the end of each chapter.

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## Product Details :

**Genre** |
: Mathematics |

**Author** |
: Helge Holden |

**Publisher** |
: Springer Science & Business Media |

**Release** |
: 2009-12-01 |

**Total Pages** |
: 305 Pages |

**ISBN** |
: 9780387894881 |

Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and parabolic) and discusses different types of random forcing. The objective is to give the reader the necessary tools to understand the proofs of existing theorems about SPDEs (from other sources) and perhaps even to formulate and prove a few new ones. Most of the material could be covered in about 40 hours of lectures, as long as not too much time is spent on the general discussion of stochastic analysis in infinite dimensions. As the subject of SPDEs is currently making the transition from the research level to that of a graduate or even undergraduate course, the book attempts to present enough exercise material to fill potential exams and homework assignments. Exercises appear throughout and are usually directly connected to the material discussed at a particular place in the text. The questions usually ask to verify something, so that the reader already knows the answer and, if pressed for time, can move on. Accordingly, no solutions are provided, but there are often hints on how to proceed. The book will be of interest to everybody working in the area of stochastic analysis, from beginning graduate students to experts in the field.

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## Product Details :

**Genre** |
: Mathematics |

**Author** |
: Sergey V. Lototsky |

**Publisher** |
: Springer |

**Release** |
: 2017-07-06 |

**Total Pages** |
: 508 Pages |

**ISBN** |
: 9783319586472 |

Learn the basics of white noise theory with White Noise Distribution Theory. This book covers the mathematical foundation and key applications of white noise theory without requiring advanced knowledge in this area. This instructive text specifically focuses on relevant application topics such as integral kernel operators, Fourier transforms, Laplacian operators, white noise integration, Feynman integrals, and positive generalized functions. Extremely well-written by one of the field's leading researchers, White Noise Distribution Theory is destined to become the definitive introductory resource on this challenging topic.

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## Product Details :

**Genre** |
: Mathematics |

**Author** |
: Hui-Hsiung Kuo |

**Publisher** |
: CRC Press |

**Release** |
: 2018-05-04 |

**Total Pages** |
: 400 Pages |

**ISBN** |
: 9781351404303 |