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- Markov evolutions and hierarchical equations in the continuum. II: multicomponent systemsPublication . Finkelshtein, Dmitri L.; Kondratiev, Yuri G.; Oliveira, Maria JoãoGeneral birth-and-death as well as hopping stochastic dynamics of infinite multicomponent particle systems in the continuum are considered. We derive the corresponding evolution equations for quasi-observables and correlation functions. We also present sufficient conditions that allow us to consider these equations on suitable Banach spaces.
- Analytic aspects of Poissonian white noise analysisPublication . Kondratiev, Yuri G.; Kuna, Tobias; Oliveira, Maria JoãoGeneral structures of Poissonian white noise analysis are presented.Simultaneously, the theory is developed on Poisson and Lebesgue- Poisson space. Both spaces have an own S-transform, well known in the Gaussian case. They give an extra connection between these two spaces via the Bargmann-Segal space. Test and generalized functions,different types of convolutions, and representations of creation and annihilation operators in the aforementioned spaces are considered.
- Extension of explicit formulas in Poissonian white noise analysis using harmonic analysis on configuration spacesPublication . Kondratiev, Yuri G.; Kuna, Tobias; Oliveira, Maria JoãoHarmonic analysis on configuration spaces is used in order to extend explicit expressions for the images of creation, annihilation, and second quantization operators in L2-spaces with respect to Poisson point processes to a set of functions larger than the space obtained by directly using chaos expansion. This permits,in particular, to derive an explicit expression for the generator of the second quantization of a sub-Markovian contraction semigroup on a set of functions which forms a core of the generator.
- Holomorphic Bogoliubov functionals for interacting particle systems in continuumPublication . Kondratiev, Yuri G.; Kuna, Tobias; Oliveira, Maria JoãoCombinatorial harmonic analysis techniques are used to develop new analytical methods for the study of interacting particle systems in continuum based on a Bogoliubov functional approach. Concrete applications of the methods are presented, namely, conditions for the existence of Bogoliubov functionals, a uniqueness result for Gibbs measures in the high temperature regime. We also propose a new approach to the study of non-equilibrium stochastic dynamics in terms of evolution equations for Bogoliubov functionals.
- On the relations between Poissonian white noise analysis and harmonic analysis on configuration spacesPublication . Kondratiev, Yuri G.; Kuna, Tobias; Oliveira, Maria JoãoWe unify techniques of Poissonian white noise analysis and harmonic analysis on configuration spaces establishing relations between the main structures of both ones. This leads to new results inside of infinite-dimensional analysis as well as in its applications to problems of mathematical physics, e.g., statistical mechanics of continuous systems.