Objetivo
"The main objective of this proposal is to study the concept of ""multi-parameter multi-fractional Brownian motion"" and its generalizations. We define this process, prove existence and give some examples. We study its properties, especially long-range memory, different kinds of properties which replace the stationarity and the self-similarity. Some integral representations will be presented and we will try to find characterizations of this process. We develop stochastic calculus for multi-parameter multi-fractional Brownian motion and different types of set-indexed martingales. We will investigate: regularity properties of stochastic integrals with respect to multi-fractional random fields; solvability and regularity of solutions of stochastic partial differential equations with fractional and multi-fractional random noise, the properties of solutions of multi-parameter stochastic differential equations with fractional fields, e.g. Holder continuity and smoothness properties; local times and occupation densities of multi-parameter fractional processes; classical problems of financial mathematics – absence of arbitrage, option pricing, optimal investment strategies, optimal exercise of American options – in a long-range dependence framework; mixed fractional/stable limit models; limit theorems for the products of random fields with weak and long range dependence and multi-fractal log-infinite divisible scenarios; formulation and characterisation of a class of spatial multi-fractional models and scaling law results for the variable-order fractional diffusion equations with random data; development of a theory of statistical estimation for the considered models. Finally, we will suggest some applied problems in which the multi-parameter multi-fractional Brownian motion can be used."
Ámbito científico (EuroSciVoc)
CORDIS clasifica los proyectos con EuroSciVoc, una taxonomía plurilingüe de ámbitos científicos, mediante un proceso semiautomático basado en técnicas de procesamiento del lenguaje natural.
CORDIS clasifica los proyectos con EuroSciVoc, una taxonomía plurilingüe de ámbitos científicos, mediante un proceso semiautomático basado en técnicas de procesamiento del lenguaje natural.
- ciencias socialeseconomía y empresaciencia económicamacroeconomía
- ciencias naturalesmatemáticasmatemáticas purasanálisis matemáticoecuaciones diferencialesecuaciones diferenciales parciales
- ciencias socialesderecho
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Palabras clave
Convocatoria de propuestas
FP7-PEOPLE-IRSES-2008
Consulte otros proyectos de esta convocatoria
Régimen de financiación
MC-IRSES - International research staff exchange scheme (IRSES)Coordinador
52900 Ramat Gan
Israel