We explore W-adaptedness, a variant of the usual notion of adaptedness found in stochastic calculus. It is shown that the (non-adapted) quantum stochastic integrals of bounded, W-adapted processes are themselves bounded and W-adapted, a fact that may be deduced from the Bismut-Clark-Ocone formula of
Stochastic processes and the evolution of quantum observables
โ Scribed by J. Bertrand; G. Rideau
- Publisher
- Springer
- Year
- 1983
- Tongue
- English
- Weight
- 361 KB
- Volume
- 7
- Category
- Article
- ISSN
- 0377-9017
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โฆ Synopsis
AB ST R ACT. The classical results of stochastic calculus are extended to the equations giving the evolution of quantum observables in terms of their Weyl symbols, when the free Hamiltonian in ho(p) + qhl (p) or (t9 2/2m) + (rnco2/2)q z and the interaction potential is the Fourier transform of a bounded measure. The arising stochastic processes are purely jump processes.
๐ SIMILAR VOLUMES
Bohm mechanics and Nelson stochastic mechanics are confronted with quantum mechanics in the presence of noninteracting subsystems. In both cases, it is shown that correlations at different times of compatible position observables on stationary states agree with quantum mechanics only in the case of