Mathematics – Probability
Scientific paper
2005-12-21
Quantum Probability and Related Topics 6 137--179 World Scientific, Singapore 1991
Mathematics
Probability
27 pages. See also related papers at http://www.maths.nott.ac.uk/personal/vpb/research/ana_cal.html http://www.maths.nott.ac
Scientific paper
A generalized definition of quantum stochastic (QS) integrals and differentials is given in the free of adaptiveness and dimensionality form in terms of Malliavin derivative on a projective Fock space, and their uniform continuity with respect to the inductive limite convergence is proved. A new form of QS calculus based on an inductive *-algebraic structure in an indefinite space is developed and a nonadaptive generalization of the QS Ito formula for its representation in Fock space is derived. The problem of solution of general QS evolution equations in a Hilbert space is solved in terms of the constructed operator representation of chronological products, defined in the indefinite space, and isometry and *-homomorphism property respectively for operators and maps of these solutions, corresponding to the peseudounitary and *-homomorphism property of the QS integrable generators is proved.
No associations
LandOfFree
A nonadapted stochastic calculus and non stationary evolution in Fock scale does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A nonadapted stochastic calculus and non stationary evolution in Fock scale, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A nonadapted stochastic calculus and non stationary evolution in Fock scale will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-726319