«Stochastic calculus»
۳۳۴۲ نتیجهQuantum Stochastic Calculus with Maximal Operator Domains1 by Stéphane Attal
Quantum stochastic calculus is extended in a new formulation in which its stochastic integrals achieve their natural and maximal domains. Operator adaptedness, conditional expectations and stochastic integrals are all defined simply in terms of the orthogonal projections of the t
Quantum Stochastic Calculus and Quantum Nonlinear Filtering
A ?algebraic inde nite structure of quantum stochastic (QS) calculus is introduced and a continuity property of generalized nonadapted QS integrals is proved under the natural integrability conditions in an in nitely dimensional nuclear space. The class of nondemolition output Q
Some Properties of Quantum Lévy Area in Fock and Non-fock Quantum Stochastic Calculus.
We consider the analogue of Lévy area, de ned as an iterated stochastic integral, obtained by replacing the two independent component onedimensional Brownian motions by the mutually non-commuting momentum and position Brownian motions P and Q of either Fock or non-Fock quantum st
A stochastic double product in non-Fock quantum stochastic calculus
Generalising the previous Fock case, we show that in an extremal universally invariant representation of the canonical commutation relations, a second quantised double product of infinitesimal rotations is a stochastic double product in the corresponding non-Fock quantum stochast
Quantum stochastic calculus applied to path spaces over Lie groups
Quantum stochastic calculus is applied to the proof of Skorokhod and Weitzenböck type identities for functionals of a Lie group-valued Brownian motion. In contrast to the case of Rd-valued paths, the computations use all three basic quantum stochastic differentials.
Forward and backward adapted quantum stochastic calculus and double product integrals
We show that iterated stochastic integrals can be described equivalently either by the conventional forward adapted, or by backward adapted quantum stochastic calculus. By using this equivalence we establish two properties of triangular (causal) and rectangular double quantum sto
Quantum Stratonovich Stochastic Calculus and the Quantum Wong-Zakai Theorem
We introduce the Stratonovich version of quantum stochastic calculus including integrals with respect to emission (creation), absorption (annihilation) and scattering (conservation) processes. The calculus allows us to consider the limit of regular open dynamical systems as a qua
Continual Measurements in Quantum Mechanics and Quantum Stochastic Calculus
2.1 Quantum stochastic calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 The Fock space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 The Weyl operators and the Bose fields . . . . . . . . . . .
On Q-deformed Quantum Stochastic Calculus
In this paper we investigate a quantum stochastic calculus build of creation, annihilation and number of particles operators which fulfill some deformed commutation relations. Namely, we introduce a deformation of a number of particles operator which has simple commutation relati
Geometry, stochastic calculus and quantum fields in a non-commutative space-time
The algebras of non-relativistic and of classical mechanics are unstable algebraic structures. Their deformation towards stable structures leads, respectively, to relativity and to quantum mechanics. Likewise, the combined relativistic quantum mechanics algebra is also unstable.