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Quantum stochastic calculus on interacting Fock spaces: semimartingale estimates and stochastic integral
Full text linkIndependence arising from interacting Fock spaces and related central limit theorem
No full textWe present the notion of projective independence, which abstracts,
in an algebraic setting, the factorization rule for the vacuum expectation
of creation-annihilations-preservation operators in interacting Fock
spaces described in [3]. Furthermore, we give a central limit theorem based
on such a notion and a Fock representation of the limit process
A projective central limit theorem and an interacting Fock space representation for the limit process
No full text
Rotation invariant Fock spaces
No full textIn this paper we give a necessary and sucient condition on the interacting Fock (IFF)
space by which the vacuum distribution of the position operator is rotation invariant
A constructive boolean central limit theorem
No full textWe give a construction of the creation, annihilation and number processes on the Boolean Fock space by means of a quantum central limit theorem starting from creation, annihilation and number processes with discrete time
Limits of Some Weighted Cesaro Averages
Full text linkWe investigate the existence of the limit of some high order
weighted Cesaro averages
Ergodic theorems in Quantum Probability: an application to the monotone stochastic processes
Full text linkWe give sufficient conditions ensuring the strong ergodic
property of unique mixing for C-dynamical systems arising
from Yang-Baxter-Hecke quantisation. We discuss whether they
can be applied to some important cases including Monotone, Boson,
Fermion and Boolean C-algebras in a unified version. The
Monotone and the Boolean cases are treated in full generality, the
Bose/Fermi cases being already widely investigated. In fact, on
one hand we show that the set of stationary stochastic processes
are isomorphic to a segment in both the Monotone and Boolean
situations, on the other hand the Boolean processes enjoy the very
strong property of unique mixing with respect to the fixed point
subalgebra and the Monotone ones do not
Distributions for Nonsymmetric Monotone and Weakly Monotone Position Operators
Full text linkWe study the vacuum distribution, under an appropriate scaling, of a family of partial
sums of nonsymmetric position operators on weakly monotone and monotone Fock
spaces, respectively. We preliminary treat the case of weaklymonotone Fock space, and
show that any single operator has the vacuum law belonging to the free Meixner class.
After establishing some relations between the combinatorics of Motzkin and Riordan
paths, we give a recursive formula for the vacuum moments of the law of any finite
sum. Since the operators are monotone independent, the distribution is the monotone
convolution of the free Meixner law above.We also investigate the asymptotic measure
for these sums, which can be seen as “Poisson type” limit law. It turns out to belong
to the free Meixner class, with an atomic and an absolutely continuous part (w.r.t. the
Lebesgue measure). Finally, we briefly apply analogous considerations to the case of
monotone Fock space
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