Quantum stochastic calculus for the uniform measure and Boolean convolution
| Nicolas Privault |
| Université de la Rochelle |
| Avenue Michel Crépeau |
| 17042 La Rochelle Cedex 1 |
| France |
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 Classification:
81S25, 46L50, 60H07, 60E05.
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