Multi-parameter Multi-fractional Brownian Motion

Projektinformationen

MULTIFRACTIONALITY

ID Finanzhilfevereinbarung: 230804

Abgeschlossenes Projekt

Startdatum 1 Januar 2009

Enddatum 31 Dezember 2012

Finanziert unter

• Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)

Gesamtkosten € 90 000,00

EU-Beitrag € 90 000,00

Koordiniert durch

BAR ILAN UNIVERSITY
Israel

Ziel

"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."

Wissenschaftliches Gebiet

• social sciences › economics and business › economics › macroeconomics
• natural sciences › mathematics › pure mathematics › mathematical analysis › differential equations › partial differential equations
• social sciences › law

Schlüsselbegriffe

• Gaussian processes
• anomalous diffusion
• local time
• long-range dependence
• multi-fractional process
• multi-parameter and set-indexed processes
• self-similarity
• spatiotemporal non-linear systems

Programm/Programme

• FP7-PEOPLE - Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)

Thema/Themen

• FP7-PEOPLE-IRSES-2008 - Marie Curie Action "International Research Staff Exchange Scheme"

Aufforderung zur Vorschlagseinreichung

FP7-PEOPLE-IRSES-2008
Andere Projekte für diesen Aufruf anzeigen

Finanzierungsplan

MC-IRSES - International research staff exchange scheme (IRSES)

Koordinator

BAR ILAN UNIVERSITY

Kontakt Verwaltung

Estelle Waise (Ms.)

• EU-Beitrag: € 90 000,00
• Adresse: BAR ILAN UNIVERSITY CAMPUS ; 52900 Ramat Gan ; Israel
• Aktivitätstyp: Higher or Secondary Education Establishments
• Gesamtkosten: Keine Daten