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Author Privault, Nicolas
Source CiteSeerX
Content type Text
File Format PDF
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Quantum Stochastic Calculus ♦ Uniform Measure ♦ Boolean Convolution ♦ Boolean Brownian ♦ Non-commutative Relation ♦ Fock Space ♦ Exponential Law ♦ Boolean Counterpart ♦ Uniform Distribution ♦ Basic Probability Law ♦ Tensor Independence ♦ Poisson Process ♦ Classical Convolution ♦ Boolean Independence ♦ Classical Setting ♦ Bernoulli Process ♦ Non-commutative Process ♦ Mathematics Subject Classication ♦ Time Change ♦ Boolean Fock Space
Abstract We study a subspace of the Fock space, called Boolean Fock space, and its associated non-commutative processes obtained by combinations of annihilators and creators. These processes include the Boolean Brownian and Poisson processes obtained by replacing the classical convolution by its Boolean counterpart, and a family of Bernoulli processes. Using a quantum stochastic calculus constructed by time changes, we complete the existing non-commutative relations between basic probability laws. In particular the uniform distribution has the role played by the exponential law in the classical setting of tensor independence. Key words: Quantum stochastic calculus, Boolean independence, uniform measure. Mathematics Subject Classication: 81S25, 46L50, 60H07, 60E05. 1
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study