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Luís da Silva, José

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5319-65EA-8C46
0000-0002-5207-1703

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1995 - 19982
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End date: 1998 × Start date: 1995 ×

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  • Studies in non-Gaussian analysis
    Publication . Silva, José Luís da
    This thesis presents general methods in non-Gaussian analysis in infinite dimensional spaces. As main applications we study Poisson and compound Poisson spaces. Given a probability measure μ on a co-nuclear space, we develop an abstract theory based on the generalized Appell systems which are bi-orthogonal. We study its properties as well as the generated Gelfand triples. As an example we consider the important case of Poisson measures. The product and Wick calculus are developed on this context. We provide formulas for the change of the generalized Appell system under a transformation of the measure. The L² structure for the Poisson measure, compound Poisson and Gamma measures are elaborated. We exhibit the chaos decomposition using the Fock isomorphism. We obtain the representation of the creation, annihilation operators. We construct two types of differential geometry on the configuration space over a differentiable manifold. These two geometries are related through the Dirichlet forms for Poisson measures as well as for its perturbations. Finally, we construct the internal geometry on the compound configurations space. In particular, the intrinsic gradient, the divergence and the Laplace-Beltrami operator. As a result, we may define the Dirichlet forms which are associated to a diffusion process. Consequently, we obtain the representation of the Lie algebra of vector fields with compact support. All these results extends directly for the marked Poisson spaces.
    1998Doctoral thesis Open access Show more
  • The Feynman integrand for the perturbed harmonic oscillator as a Hida distribution
    Publication . Cunha, Mário; Drumond, Custódia; Leukert, Peter; Silva, José Luís; Westerkamp, Werner
    We rwiew some basic notions and results of White Noise Analysis that are used in the con struction of the Feynman integrand as a generalized White Noise functional. We show that the Feyn man integrand for the harmonic oscillator in an external potential is a Hida distri
    1995Journal article Open access Show more