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- Self-repelling fractional Brownian motion : a generalized Edwards model for chain polymersPublication . Bornales, Jinky; Oliveira, Maria João; Streit, LudwigWe present an extension of the Edwards model for conformations of individual chain molecules in solvents in terms of fractional Brownian motion, and discuss the excluded volume effect on the end-to-end length of such trajectories or molecules.
- Intersection local times of independent fractional Brownian motions as generalized white noise functionalsPublication . Oliveira, Maria João; Silva, José Luís da; Streit, LudwigIn this work we present expansions of intersection local times of fractional Brownian motions in R^d , for any dimension d ≥ 1, with arbitrary Hurst coefficients in (0, 1)^d . The expansions are in terms of Wick powers of white noises (corresponding to multiple Wiener integrals), being well-defined in the sense of generalized white noise functionals. As an application of our approach, a sufficient condition on d for the existence of intersection local times in L^2 is derived, extending the results in Nualart and Ortiz-Latorre (J. Theoret. Probab. 20(4):759–767, 2007) to different and more general Hurst coefficients.
- Fractional Brownian polymers : some first resultsPublication . Bornales, Jinky; Eleutério, Samuel; Oliveira, Maria João; Streit, LudwigRecently the Edwards model for chain polymers in good solvents has been extended to include fractional Brownian motion trajectories as a description of polymer conformations. This raises in particular the question of the corresponding Flory formula for the end-to-end length of those molecules. A generalized Flory formula has been proposed, and there are some first results of numerical validations.