| Item type | Current location | Collection | Call number | Copy number | Status | Date due | Barcode |
|---|---|---|---|---|---|---|---|
| E-Books | Biblioteca da FCTUNL Online | Não Ficção | QA273.SPR FCT 97274 (Browse shelf) | 1 | Available |
Browsing Biblioteca da FCTUNL Shelves , Shelving location: Online , Collection code: Não Ficção Close shelf browser
| QA273.SPR FCT 97017 Random walks on reductive groups | QA273.SPR FCT 97028 Mod-ϕ convergence | QA273.SPR FCT 97194 Rabi N. Bhattacharya | QA273.SPR FCT 97274 The parabolic Anderson model | QA273.SPR FCT 97281 From Lévy-type processes to parabolic SPDEs | QA273.SPR FCT 97336 Asymptotic analysis for functional stochastic differential equations | QA273.SPR FCT 97338 Stochastic and infinite dimensional analysis |
Colocação: Online
This is a comprehensive survey on the research on the parabolic Anderson model – the heat equation with random potential or the random walk in random potential – of the years 1990 – 2015. The investigation of this model requires a combination of tools from probability (large deviations, extreme-value theory, e.g.) and analysis (spectral theory for the Laplace operator with potential, variational analysis, e.g.). We explain the background, the applications, the questions and the connections with other models and formulate the most relevant results on the long-time behavior of the solution, like quenched and annealed asymptotics for the total mass, intermittency, confinement and concentration properties and mass flow. Furthermore, we explain the most successful proof methods and give a list of open research problems. Proofs are not detailed, but concisely outlined and commented; the formulations of some theorems are slightly simplified for better comprehension.
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