Obiettivo
"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."
Campo scientifico (EuroSciVoc)
CORDIS classifica i progetti con EuroSciVoc, una tassonomia multilingue dei campi scientifici, attraverso un processo semi-automatico basato su tecniche NLP.
CORDIS classifica i progetti con EuroSciVoc, una tassonomia multilingue dei campi scientifici, attraverso un processo semi-automatico basato su tecniche NLP.
- scienze socialieconomia e commercioscienze economichemacroeconomia
- scienze naturalimatematicamatematica puraanalisi matematicaequazioni differenzialiequazioni differenziali parziali
- scienze socialilegge
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FP7-PEOPLE-IRSES-2008
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MC-IRSES - International research staff exchange scheme (IRSES)Coordinatore
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