Infinite Dimensional Analysis Quantum Probability and Related Topics · 1999 · 13 citations · 7 references
EngineeringProperty LawProbability TheoryStochastic ProcessesEigenvalue ProblemsHilbert Space FormalismLévy ProcessesOperator TheoryPoisson ProcessesStochastic CalculusEigenvalues Of The LaplacianPoisson's EquationSelf-adjoint Eigenvalue ProblemsSelf-adjoint Operators
In this paper we shall discuss the Lévy Laplacian acting on the space of Poisson noise functionals. We give eigenfunctions of the Laplacian and extend the operator to a self-adjoint operator densely defined on some Hilbert space.
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Generalized Poisson Functionals
Yoshifusa Ito · Probability Theory and Related Fields · 1988 · 107 citations · Full text
Calculus on Gaussian and Poisson white noises
Yoshifusa Ito, Izumi Kubo · Nagoya Mathematical Journal · 1988 · 88 citations · Full text
Engineering, Mathematics, Physics +10