03283nam 2200601 450 991048061120332120170821172555.01-4704-0095-2(CKB)3360000000464702(EBL)3113938(SSID)ssj0000889138(PQKBManifestationID)11497173(PQKBTitleCode)TC0000889138(PQKBWorkID)10875529(PQKB)10502085(MiAaPQ)EBC3113938(PPN)195414012(EXLCZ)99336000000046470220140909h19941994 uy 0engur|n|---|||||txtccrParabolic Anderson problem and intermittency /René A. Carmona, S. A. MolchanovProvidence, Rhode Island :American Mathematical Society,1994.©19941 online resource (138 p.)Memoirs of the American Mathematical Society,0065-9266 ;Number 518"March 1994, Volume 108, Number 518 (third of 5 numbers)."0-8218-2577-1 Includes bibliographical references.""CONTENTS""; ""I: INTRODUCTION""; ""II: EXISTENCE AND UNIQUENESS PROBLEMS""; ""II.1 The Deterministic Problem""; ""II.1.1 The Feynmanâ€?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 Feynmanâ€?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)](Ï?)""; ""III.2.2 Estimation of γ[sub(p)](Ï?)/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""Memoirs of the American Mathematical Society ;Number 518.Stochastic partial differential equationsRandom operatorsGaussian processesElectronic books.Stochastic partial differential equations.Random operators.Gaussian processes.519.2Carmona R(René),974545Molchanov S. A(Stanislav A.),MiAaPQMiAaPQMiAaPQBOOK9910480611203321Parabolic Anderson problem and intermittency2218893UNINA