Wilfried Grossmann

Georg Ch. Pflug

Wolfgang Wertz

The interaction of various ideas from different researchers provides a main impetus to mathematical prosress. An important way to make communication possible is through international conferences on more or less spezialized topics~ The existence of several centers for research in probabil ity and statistics in the eastern part of central Europe - somewhat vaguely described as the Pannonian area - led to the idea of organizing Pannonian Symposia on Mathematical Statistics (PS~1S). The second such symposium was held at Bad Tatzmannsdorf, Burgenland (Austria), from 14 to 20 June 1981. About 100 researchers from 13 countries participated in that event and about 70 papers were delivered. Most of the papers dealt with one of the following topics: nonparametric estimation theory, asymptotic theory of estimation, invariance principles, limit theorems and aoplications. Full versions of selected papers, all presenting new results are included in this volume. The editors take this opportunity to thank the following institutions for their assistance in making the conference possible: the Provincial Government of Burgenland, the Austrian Ministry for Research and Science, the Burgenland Chamber of Commerce, the Control Data Corporation, the Austrian Society for Statistics and Informatics, the Landes hypothekenbank Burgenland, the Volksbank Oberwart, and the Community and Kurbad AG of Bad Tatzmannsdorf. We are also greatly indebted to all those persons who helped in editing this volume and in particular to the vii W. Grossmann et al. reds.), Probability and Statistical Inference, vii-viii.

Proceedings of the 2nd Pannonian Symposium on Mathematical Statistics, Bad Tatzmannsdorf, Austria, June 14–20, 1981

Probability and Statistical Inference

Kurt Marti

Yuri Ermoliev

Uncertainties and changes are pervasive characteristics of modern systems involving interactions between humans, economics, nature and technology. These systems are often too complex to allow for precise evaluations and, as a result, the lack of proper management (control) may create significant risks. In order to develop robust strategies we need approaches which explic itly deal with uncertainties, risks and changing conditions. One rather general approach is to characterize (explicitly or implicitly) uncertainties by objec tive or subjective probabilities (measures of confidence or belief). This leads us to stochastic optimization problems which can rarely be solved by using the standard deterministic optimization and optimal control methods. In the stochastic optimization the accent is on problems with a large number of deci sion and random variables, and consequently the focus ofattention is directed to efficient solution procedures rather than to (analytical) closed-form solu tions. Objective and constraint functions of dynamic stochastic optimization problems have the form of multidimensional integrals of rather involved in that may have a nonsmooth and even discontinuous character - the tegrands typical situation for "hit-or-miss" type of decision making problems involving irreversibility ofdecisions or/and abrupt changes ofthe system. In general, the exact evaluation of such functions (as is assumed in the standard optimization and control theory) is practically impossible. Also, the problem does not often possess the separability properties that allow to derive the standard in control theory recursive (Bellman) equations.

Georg Ch. Pflug

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