Loading...
11 results
Search Results
Now showing 1 - 10 of 11
- 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.
- Polymer measure: varadhan's renormalization revisitedPublication . Bock, Wolfgang; Oliveira, Maria João; Silva, José Luís da; Streit, LudwigThrough chaos decomposition we improve the Varadhan estimate for the rate of convergence of the centered approximate self-intersection local time of planar Brownian motion.
- Intersection local times of independent Brownian motions as generalized white noise functionalsPublication . Albeverio, Sergio; Oliveira, Maria João; Streit, LudwigA "chaos expansion" of the intersection local time functional of two independent Brownian motions in Rd is given. The expansion is in terms of normal products of white noise (corresponding to multiple Wiener integrals). As a consequence of the local structure of the normal products, the kernel functions in the expansion are explicitly given and exhibit clearly the dimension dependent singularities of the local time functional. Their Lp-properties are discussed. An important tool for deriving the chaos expansion is a computation of the "S-transform" of the corresponding regularized intersection local times and a control about their singular limit.
- Self-avoiding fractional Brownian motion: the Edwards modelPublication . Grothaus, Martin; Oliveira, Maria João; Silva, José Luís da; Streit, LudwigIn this work we extend Varadhan’s construction of the Edwards polymer model to the case of fractional Brownian motions in Rd , for any dimension d ≥ 2, with arbitrary Hurst parameters H ≤ 1/d.
- Feynman integrals for non-smooth and rapidly growing potentialsPublication . Faria, Margarida de; Oliveira, Maria João; Streit, LudwigThe Feynman integral for the Schrödinger propagator is constructed as a generalized function of white noise, for a linear space of potentials spanned by finite signed measures of bounded support and Laplace transforms of such measures, i.e., locally singular as well as rapidly growing at infinity. Remarkably, all these propagators admit a perturbation expansion.
- Results about the free kawasaki dynamics of continuous particle systems in infinite volume: long-time asymptotics and hydrodynamic limitPublication . Kondratiev, Yuri G.; Kuna, Tobias; Oliveira, Maria João; Silva, José Luís da; Streit, LudwigAn infinite particle system of independent jumping particles in infinite volume is considered. Their construction is recalled, further properties are derived, the relation with hierarchical equations, Poissonian analysis, and second quantization are discussed. The hydrodynamic limit for a general initial distribution satisfying a mixing condition is derived. The long-time asymptotics is computed under an extra assumption. The relation with constructions based on infinite volume limits is discussed.
- 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.
- Sheffer homeomorphisms of spaces of entire functions in infinite dimensional analysisPublication . Finkelshtein, Dmitri L.; Kondratiev, Yuri G.; Lytvynov, Eugene; Oliveira, Maria João; Streit, LudwigFor certain Sheffer sequences $(s_n)_{n=0}^\infty$ on $\mathbb C$, Grabiner (1988) proved that, for each $\alpha\in[0,1]$, the corresponding Sheffer operator $z^n\mapsto s_n(z)$ extends to a linear self-homeomorphism of $\mathcal E^{\alpha}_{\mathrm{min}}(\mathbb C)$, the Fréchet topological space of entire functions of exponential order $\alpha$ and minimal type. In particular, every function $f\in \mathcal E^{\alpha}_{\mathrm{min}}(\mathbb C)$ admits a unique decomposition $f(z)=\sum_{n=0}^\infty c_n s_n(z)$, and the series converges in the topology of $\mathcal E^{\alpha}_{\mathrm{min}}(\mathbb C)$. Within the context of a complex nuclear space $\Phi$ and its dual space $\Phi'$, in this work we generalize Grabiner's result to the case of Sheffer operators corresponding to Sheffer sequences on $\Phi'$. In particular, for $\Phi=\Phi'=\mathbb C^n$ with $n\ge2$, we obtain the multivariate extension of Grabiner's theorem. Furthermore, for an Appell sequence on a general co-nuclear space $\Phi'$, we find a sufficient condition for the corresponding Sheffer operator to extend to a linear self-homeomorphism of $\mathcal E^{\alpha}_{\mathrm{min}}(\Phi')$ when $\alpha>1$. The latter result is new even in the one-dimensional case.
- 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.
- A generalized clark-ocone formulaPublication . Faria, Margarida de; Oliveira, Maria João; Streit, LudwigWe extend the Clark-Ocone formula to a suitable class of generalized Brownian functionals. As an example we derive a representation of Donsker's delta function as (limit of) a stochastic integral.