MULTIFRACTIONALITY (230804)

  https://cordis.europa.eu/project/id/230804

  FP7 (2007-2013)

  Multi-parameter Multi-fractional Brownian Motion

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

  macroeconomics  ·  partial differential equations  ·  law

  2009-01-01 Start Date (YY-MM-DD)

  2012-12-31 End Date (YY-MM-DD)

  € 90,000 Total Cost

  Description

'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.'

  Complicit Organisations

1 Israeli organisation participates in MULTIFRACTIONALITY.