MULTIFRACTIONALITY
Multi-parameter Multi-fractional Brownian Motion
| Coordinatore |
Organization address
address: BAR ILAN UNIVERSITY CAMPUS contact info |
| Nazionalità Coordinatore | Non specificata |
| Totale costo | 90˙000 € |
| EC contributo | 90˙000 € |
| Programma | FP7-PEOPLE
Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) |
| Code Call | FP7-PEOPLE-IRSES-20 |
| Anno di inizio | 2009 |
| Periodo (anno-mese-giorno) | 2009-01-01 - 2012-12-31 |
Partecipanti
| # | ||||
|---|---|---|---|---|
| 1 |
BAR ILAN UNIVERSITY
Organization address
address: BAR ILAN UNIVERSITY CAMPUS contact info |
IL (RAMAT GAN) | coordinator | 90˙000.00 |
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Obiettivo del progetto (Objective)
'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.'