Theory of stochastic NMR spectroscopy. Application of the ITÔ and Stratonovich calculus
ABSTRACT 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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ABSTRACT: INTRODUCTION There are marine mammals, such as elephant seals, that travel great distances and are tracked. It is of interest to biologists to describe the routes. One can wonder for example if the animals follow great circle paths. The animals will be foraging along the way, i.e. pulled away from the direct route from origin to destination, and this may be modelled as stochastic fluctuations. The great circle route is the geodesic, providing the shortest trip. A ship needs to be changing course continually to stay ____________ 1 Statistics Department, University of California, Berkeley, CA 94720-3860, USA - 2 - on it. It is intriguing that some animals apparently do not need to change course, they can keep going straight ahead. An issue that arises in modelling the physical world is whether to work employing the Ito or the Stratonovich calculus. Reasons have been presented various places to the effect that when developing physical a01/1997;
- Data Handling in Science and Technology 01/1996; 18:489-512.
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ABSTRACT: Consider a particle moving on the surface of the unit sphere in R 3 and heading towards a specific destination with a constant average speed, but subject to random deviations. The motion is modeled as a diffusion with drift restricted to the surface of the sphere. Expressions are set down for various characteristics of the process including expected travel time to a cap, the limiting distribution, the likelihood ratio and some estimates for parameters appearing in the model.Journal of Theoretical Probability 03/1997; 10(2):429-443. · 0.55 Impact Factor