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Parabolic Anderson Problem and Intermittency.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical SocietyPublisher: Providence : American Mathematical Society, 1994Copyright date: ©1994Edition: 1st edDescription: 1 online resource (138 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781470400958
Subject(s): Genre/Form: Additional physical formats: Print version:: Parabolic Anderson Problem and IntermittencyDDC classification:
  • 519.2
LOC classification:
  • QA274.25 -- .C376 1994eb
Online resources:
Contents:
Intro -- CONTENTS -- I: INTRODUCTION -- II: EXISTENCE AND UNIQUENESS PROBLEMS -- II.1 The Deterministic Problem -- II.1.1 The Feynman-Kac Representation -- II.1.2 Special Notations -- II.1.3 Existence Problems -- II.1.4 Uniqueness -- II.2 The Random Case -- II.2.1 Setting of the Problem -- II.2.2 Continuity of the Feynman-Kac Formula -- II.2.3 The Case of a Homogeneous Potential Field -- II.2.4 The Case of a White Noise Potential -- II.2.5 A Diffusion Limit Approximation Result -- II.3 Existence and Equations for the Moments -- III: MOMENT LYAPUNOV EXPONENTS AND INTERMITTENCY -- III.1 The White Noise Case -- III.1.1 Existence of the Moment Lyapunov Exponents -- III.1.2 An Explicitly Solvable Model -- III.1.3 First General Properties -- III.1.4 Small k Behavior of γ[sub(p)](K) -- III.1.5 Large K Behavior of γ[sub(p)](K) -- III.1.6 Asymptotic Behavior of the Critical Diffusion Constant -- III.1.7 Summary -- III.2 The Case of Finite Correlation Length -- III.2.1 Existence of γ[sub(p)](σ) -- III.2.2 Estimation of γ[sub(p)](σ)/P -- III.2.3 Continuity Results -- III.2.4 Lyapunov Exponents as Functions of K -- III.2.5 Another Explicitly Solvable Model -- IV: ALMOST SURE LYAPUNOV EXPONENTS -- IV.1 Existence -- IV.2 Proof of the Lower Bound -- IV.3 Proof of the Upper Bound -- V: CONCLUDING REMARKS.
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Intro -- CONTENTS -- I: INTRODUCTION -- II: EXISTENCE AND UNIQUENESS PROBLEMS -- II.1 The Deterministic Problem -- II.1.1 The Feynman-Kac Representation -- II.1.2 Special Notations -- II.1.3 Existence Problems -- II.1.4 Uniqueness -- II.2 The Random Case -- II.2.1 Setting of the Problem -- II.2.2 Continuity of the Feynman-Kac Formula -- II.2.3 The Case of a Homogeneous Potential Field -- II.2.4 The Case of a White Noise Potential -- II.2.5 A Diffusion Limit Approximation Result -- II.3 Existence and Equations for the Moments -- III: MOMENT LYAPUNOV EXPONENTS AND INTERMITTENCY -- III.1 The White Noise Case -- III.1.1 Existence of the Moment Lyapunov Exponents -- III.1.2 An Explicitly Solvable Model -- III.1.3 First General Properties -- III.1.4 Small k Behavior of γ[sub(p)](K) -- III.1.5 Large K Behavior of γ[sub(p)](K) -- III.1.6 Asymptotic Behavior of the Critical Diffusion Constant -- III.1.7 Summary -- III.2 The Case of Finite Correlation Length -- III.2.1 Existence of γ[sub(p)](σ) -- III.2.2 Estimation of γ[sub(p)](σ)/P -- III.2.3 Continuity Results -- III.2.4 Lyapunov Exponents as Functions of K -- III.2.5 Another Explicitly Solvable Model -- IV: ALMOST SURE LYAPUNOV EXPONENTS -- IV.1 Existence -- IV.2 Proof of the Lower Bound -- IV.3 Proof of the Upper Bound -- V: CONCLUDING REMARKS.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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