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- 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.
- Stochastic and infinite dimensional analysisPublication . Bernido, Christopher C.; Carpio-Bernido, Maria Victoria; Grothaus, Martin; Kuna, Tobias; Oliveira, Maria João; Silva, José Luís daThis volume presents a collection of papers covering applications from a wide range of systems with infinitely many degrees of freedom studied using techniques from stochastic and infinite dimensional analysis, e.g. Feynman path integrals, the statistical mechanics of polymer chains, complex networks, and quantum field theory. Systems of infinitely many degrees of freedom create their particular mathematical challenges which have been addressed by different mathematical theories, namely in the theories of stochastic processes, Malliavin calculus, and especially white noise analysis. These proceedings are inspired by a conference held on the occasion of Prof. Ludwig Streit’s 75th birthday and celebrate his pioneering and ongoing work in these fields.
- 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.
- 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.
- 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.
- Chaos decomposition and gap renormalization of brownian self-intersection local timesPublication . Bornales, Jinky; Oliveira, Maria João; Streit, LudwigWe study the chaos decomposition of self-intersection local times and their regularization, with a particular view towards Varadhan's renormalization for the planar Edwards model.