Stochastic Processes

M. Girault

2012년 12월 · Springer Science & Business Media

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Existing works on stochastic processes belong to a field of abstract mathematics which puts them beyond the scope of the non-specialist. The preoccupations of research mathematicians being more often than not distant from the practical problems of experimental methodology, the needs of practical workers, though real, are not met by the majority of works that. deal with processes. By "practical workers", we mean research scientists in all the different disciplines: Physics, Chemistry, Biology, Medicine, Population, Economics, Organisation, Operational Research etc. Indeed, all scientific research today touches upon complex fields in which deterministic models can be useful for no more than an element ary and simple approximation. The Calculus of Probability although offering some interesting models is still inadequate in many instances, particularly in the study of evolving systems. The practical worker must therefore have at his disposal a set of original and varied stochastic models. These models must not be too general, for in that case not only would their theoretical study prove difficult, but above all the adaptation of such models to an observed system would lead to an estimation of a great number of parameters on the basis of a necessarily restricted sample. This would constitute an insuperable difficulty for the practical scientist. It is therefore essential for him to have at his disposal a varied range of very characteristic models.