Theory of stochastic NMR spectroscopy. Application of the ITÔ and Stratonovich calculus

Laboratorium fūr physikalische Chemie, Eidgenössische Technische Hochschule, 8006 Zurich, Switzerland
Chemical Physics (Impact Factor: 1.65). 12/1976; 18(1-2):57-84. DOI: 10.1016/0301-0104(76)87037-1


The theory of stochastic differential equations is used to give a new description of a stochastic NMR experiment. It replaces an earlier approach, which was based on Wiener's orthogonal expansion of the stochastic response. For the first time, the saturation behaviour in cross and power spectra is predicted correctly. A numerical experiment confirms the theoretical results. The relative signal intensities in a stochastic resonance spectrum are calculated and compared with those obtained in a slow passage experiment. Conditions for equal relative intensities are given for various experimental situations.

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    • "Reasons have been presented various places to the effect that when developing physical applications it is simpler to start with the Stratonovich form and then switch to the Itô for developing properties of the process. See the discussions in: Bartholdi et al. (1976), Mortensen (1969), Sussman (1978), Karlin and Taylor (1981). "
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