NATO Advanced Study Institute

Probabilistic and Stochastic Methods in Analysis with Applications

July 14-27, 1991,   Il Ciocco, Italy

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	Purpose
	The Institute considered several important aspects of both pure and applied probability and stochastic processes. Use of these methods in the study of wavelets and fractals was the subject of the initial portion of the meeting. Important results in image processing, spectral estimation, singularity detection, dynamical systems, and fuzzy sets were discussed here. The second session dealt with applications of probabilistic and stochastic methods in engineering. The topics covered included signal analysis, various sampling methods, spectral analysis, holography, and tomography. Two specific talks, which elicited enthusiastic responses because of their novelty to most participants, involved the applications of random fields to environmental research, and the use of neural networks in pattern recognition. Applications in mathematics and computer science was the subject of the third session. Here the participants learned about probabilistic methods used to attack extremal problems in Fourier analysis, the location of fixed points in mixed spectrum analysis, and the identification of unknown parameters in exponential sums. A significant application of randomness in the emerging field of parallel computation was particularly interesting. The fourth and final session considered the stochastic calculus. Participants with specialties in other areas were especially enthused by the clear introductions to different aspects of this complicated subject given by the two principal lecturers. An important scientific contribution of the Institute was the further creation of a dynamic interaction between the usually disparate communities of pure and applied probabilists and analysts. From wavelets to fractals to quantum holography to stochastic optimal control, each group benefited significantly from their exposure, in many cases for the first time, to those scientists on the other end of the spectrum.
	Acknowledgements
	We wish to thank the following for their contribution to the success of this conference:
	NATO Scientific & Environmental Affairs Division
	U.S. Air Force EOARD
	National Science Foundation
	Prometheus Inc.